Lectures on Lie Algebras
Identifieur interne : 002050 ( Istex/Corpus ); précédent : 002049; suivant : 002051Lectures on Lie Algebras
Auteurs : Joseph BernsteinSource :
Abstract
Abstract: This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.
Url:
DOI: 10.1007/978-0-8176-4817-6_6
Links to Exploration step
ISTEX:9EE251B78CD16DD2DAD8A63F7EBF2669D0695470Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Lectures on Lie Algebras</title>
<author><name sortKey="Bernstein, Joseph" sort="Bernstein, Joseph" uniqKey="Bernstein J" first="Joseph" last="Bernstein">Joseph Bernstein</name>
<affiliation><mods:affiliation>Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail: bernstei@math.tau.ac.il</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:9EE251B78CD16DD2DAD8A63F7EBF2669D0695470</idno>
<date when="2012" year="2012">2012</date>
<idno type="doi">10.1007/978-0-8176-4817-6_6</idno>
<idno type="url">https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">002050</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002050</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Lectures on Lie Algebras</title>
<author><name sortKey="Bernstein, Joseph" sort="Bernstein, Joseph" uniqKey="Bernstein J" first="Joseph" last="Bernstein">Joseph Bernstein</name>
<affiliation><mods:affiliation>Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail: bernstei@math.tau.ac.il</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.</div>
</front>
</TEI>
<istex><corpusName>springer-ebooks</corpusName>
<editor><json:item><name>Bernhard Krötz</name>
<affiliations><json:string>, Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany</json:string>
<json:string>E-mail: kroetz@math.uni-hannover.de</json:string>
</affiliations>
</json:item>
<json:item><name>Omer Offen</name>
<affiliations><json:string>, Department of Mathematics, Technion-Israel Institute of Technology, 3200, Haifa, Israel</json:string>
<json:string>E-mail: offen@tx.technion.ac.il</json:string>
</affiliations>
</json:item>
<json:item><name>Eitan Sayag</name>
<affiliations><json:string>, Department of Mathematics, Ben-Gurion University of the Negev, 84105, Be'er Sheva, Israel</json:string>
<json:string>E-mail: sayage@math.bgu.ac.il</json:string>
</affiliations>
</json:item>
</editor>
<author><json:item><name>Joseph Bernstein</name>
<affiliations><json:string>Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel</json:string>
<json:string>E-mail: bernstei@math.tau.ac.il</json:string>
</affiliations>
</json:item>
</author>
<arkIstex>ark:/67375/HCB-9MDS7LTZ-D</arkIstex>
<language><json:string>eng</json:string>
</language>
<originalGenre><json:string>chapter</json:string>
</originalGenre>
<abstract>Abstract: This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.</abstract>
<qualityIndicators><refBibsNative>false</refBibsNative>
<abstractWordCount>55</abstractWordCount>
<abstractCharCount>377</abstractCharCount>
<keywordCount>0</keywordCount>
<score>7.66</score>
<pdfWordCount>12941</pdfWordCount>
<pdfCharCount>54968</pdfCharCount>
<pdfVersion>1.4</pdfVersion>
<pdfPageCount>36</pdfPageCount>
<pdfPageSize>439.37 x 666.142 pts</pdfPageSize>
</qualityIndicators>
<title>Lectures on Lie Algebras</title>
<chapterId><json:string>6</json:string>
<json:string>b978-0-8176-4817-6_6</json:string>
</chapterId>
<genre><json:string>chapter</json:string>
</genre>
<host><title>Representation Theory, Complex Analysis, and Integral Geometry</title>
<language><json:string>unknown</json:string>
</language>
<copyrightDate>2012</copyrightDate>
<doi><json:string>10.1007/978-0-8176-4817-6</json:string>
</doi>
<eisbn><json:string>978-0-8176-4817-6</json:string>
</eisbn>
<bookId><json:string>978-0-8176-4817-6</json:string>
</bookId>
<isbn><json:string>978-0-8176-4816-9</json:string>
</isbn>
<pages><first>97</first>
<last>132</last>
</pages>
<genre><json:string>book</json:string>
</genre>
<editor><json:item><name>Bernhard Krötz</name>
<affiliations><json:string>, Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany</json:string>
<json:string>E-mail: kroetz@math.uni-hannover.de</json:string>
</affiliations>
</json:item>
<json:item><name>Omer Offen</name>
<affiliations><json:string>, Department of Mathematics, Technion-Israel Institute of Technology, 3200, Haifa, Israel</json:string>
<json:string>E-mail: offen@tx.technion.ac.il</json:string>
</affiliations>
</json:item>
<json:item><name>Eitan Sayag</name>
<affiliations><json:string>, Department of Mathematics, Ben-Gurion University of the Negev, 84105, Be'er Sheva, Israel</json:string>
<json:string>E-mail: sayage@math.bgu.ac.il</json:string>
</affiliations>
</json:item>
</editor>
<subject><json:item><value>Mathematics and Statistics</value>
</json:item>
<json:item><value>Mathematics</value>
</json:item>
<json:item><value>Group Theory and Generalizations</value>
</json:item>
<json:item><value>Topological Groups, Lie Groups</value>
</json:item>
<json:item><value>Analysis</value>
</json:item>
<json:item><value>Differential Geometry</value>
</json:item>
<json:item><value>Algebra</value>
</json:item>
<json:item><value>Number Theory</value>
</json:item>
</subject>
</host>
<ark><json:string>ark:/67375/HCB-9MDS7LTZ-D</json:string>
</ark>
<publicationDate>2011</publicationDate>
<copyrightDate>2012</copyrightDate>
<doi><json:string>10.1007/978-0-8176-4817-6_6</json:string>
</doi>
<id>9EE251B78CD16DD2DAD8A63F7EBF2669D0695470</id>
<score>1</score>
<fulltext><json:item><extension>pdf</extension>
<original>true</original>
<mimetype>application/pdf</mimetype>
<uri>https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/fulltext/pdf</uri>
</json:item>
<json:item><extension>zip</extension>
<original>false</original>
<mimetype>application/zip</mimetype>
<uri>https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/fulltext/zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Lectures on Lie Algebras</title>
<respStmt><resp>Références bibliographiques récupérées via GROBID</resp>
<name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name>
</respStmt>
</titleStmt>
<publicationStmt><authority>ISTEX</authority>
<publisher scheme="https://publisher-list.data.istex.fr">Birkhäuser Boston</publisher>
<pubPlace>Boston</pubPlace>
<availability><licence><p>Springer Science+Business Media, LLC, 2012</p>
</licence>
<p scheme="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</p>
</availability>
<date>2012</date>
</publicationStmt>
<notesStmt><note type="chapter" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-CGT4WMJM-6">chapter</note>
<note type="book" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-5WTPMB5N-F">book</note>
</notesStmt>
<sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Lectures on Lie Algebras</title>
<author xml:id="author-0000" corresp="yes"><persName><forename type="first">Joseph</forename>
<surname>Bernstein</surname>
</persName>
<email>bernstei@math.tau.ac.il</email>
<affiliation>Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel</affiliation>
</author>
<editor xml:id="author-0001"><persName><forename type="first">Bernhard</forename>
<surname>Krötz</surname>
</persName>
<email>kroetz@math.uni-hannover.de</email>
<affiliation>, Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany</affiliation>
</editor>
<editor xml:id="author-0002"><persName><forename type="first">Omer</forename>
<surname>Offen</surname>
</persName>
<email>offen@tx.technion.ac.il</email>
<affiliation>, Department of Mathematics, Technion-Israel Institute of Technology, 3200, Haifa, Israel</affiliation>
</editor>
<editor xml:id="author-0003"><persName><forename type="first">Eitan</forename>
<surname>Sayag</surname>
</persName>
<email>sayage@math.bgu.ac.il</email>
<affiliation>, Department of Mathematics, Ben-Gurion University of the Negev, 84105, Be'er Sheva, Israel</affiliation>
</editor>
<idno type="istex">9EE251B78CD16DD2DAD8A63F7EBF2669D0695470</idno>
<idno type="ark">ark:/67375/HCB-9MDS7LTZ-D</idno>
<idno type="DOI">10.1007/978-0-8176-4817-6_6</idno>
<idno type="ChapterID">6</idno>
<idno type="ChapterID">b978-0-8176-4817-6_6</idno>
</analytic>
<monogr><title level="m">Representation Theory, Complex Analysis, and Integral Geometry</title>
<idno type="DOI">10.1007/978-0-8176-4817-6</idno>
<idno type="pISBN">978-0-8176-4816-9</idno>
<idno type="eISBN">978-0-8176-4817-6</idno>
<idno type="book-title-id">159517</idno>
<idno type="book-id">978-0-8176-4817-6</idno>
<idno type="book-chapter-count">10</idno>
<editor xml:id="book-author-0000"><persName><forename type="first">Bernhard</forename>
<surname>Krötz</surname>
</persName>
<email>kroetz@math.uni-hannover.de</email>
<affiliation>, Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany</affiliation>
</editor>
<editor xml:id="book-author-0001"><persName><forename type="first">Omer</forename>
<surname>Offen</surname>
</persName>
<email>offen@tx.technion.ac.il</email>
<affiliation>, Department of Mathematics, Technion-Israel Institute of Technology, 3200, Haifa, Israel</affiliation>
</editor>
<editor xml:id="book-author-0002"><persName><forename type="first">Eitan</forename>
<surname>Sayag</surname>
</persName>
<email>sayage@math.bgu.ac.il</email>
<affiliation>, Department of Mathematics, Ben-Gurion University of the Negev, 84105, Be'er Sheva, Israel</affiliation>
</editor>
<imprint><publisher>Birkhäuser Boston</publisher>
<pubPlace>Boston</pubPlace>
<date type="published" when="2011-11-07"></date>
<biblScope unit="page" from="97">97</biblScope>
<biblScope unit="page" to="132">132</biblScope>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><creation><date>2012</date>
</creation>
<langUsage><language ident="en">en</language>
</langUsage>
<abstract xml:lang="en"><p>Abstract: This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.</p>
</abstract>
<textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11649</label>
<item><term>Mathematics and Statistics</term>
</item>
</list>
</keywords>
</textClass>
<textClass><keywords scheme="Book-Subject-Group"><list><label>SCM</label>
<label>SCM11078</label>
<label>SCM11132</label>
<label>SCM12007</label>
<label>SCM21022</label>
<label>SCM11000</label>
<label>SCM25001</label>
<item><term>Mathematics</term>
</item>
<item><term>Group Theory and Generalizations</term>
</item>
<item><term>Topological Groups, Lie Groups</term>
</item>
<item><term>Analysis</term>
</item>
<item><term>Differential Geometry</term>
</item>
<item><term>Algebra</term>
</item>
<item><term>Number Theory</term>
</item>
</list>
</keywords>
</textClass>
</profileDesc>
<revisionDesc><change when="2011-11-07">Published</change>
<change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-11-28">References added</change>
</revisionDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item><extension>txt</extension>
<original>false</original>
<mimetype>text/plain</mimetype>
<uri>https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/fulltext/txt</uri>
</json:item>
</fulltext>
<metadata><istex:metadataXml wicri:clean="corpus springer-ebooks not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration>
<istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType>
<istex:document><Publisher><PublisherInfo><PublisherName>Birkhäuser Boston</PublisherName>
<PublisherLocation>Boston</PublisherLocation>
</PublisherInfo>
<Book Language="En" OutputMedium="All"><BookInfo BookProductType="Contributed volume" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><BookID>978-0-8176-4817-6</BookID>
<BookTitle>Representation Theory, Complex Analysis, and Integral Geometry</BookTitle>
<BookDOI>10.1007/978-0-8176-4817-6</BookDOI>
<BookTitleID>159517</BookTitleID>
<BookPrintISBN>978-0-8176-4816-9</BookPrintISBN>
<BookElectronicISBN>978-0-8176-4817-6</BookElectronicISBN>
<BookChapterCount>10</BookChapterCount>
<BookCopyright><CopyrightHolderName>Springer Science+Business Media, LLC</CopyrightHolderName>
<CopyrightYear>2012</CopyrightYear>
</BookCopyright>
<BookSubjectGroup><BookSubject Code="SCM" Type="Primary">Mathematics</BookSubject>
<BookSubject Code="SCM11078" Priority="1" Type="Secondary">Group Theory and Generalizations</BookSubject>
<BookSubject Code="SCM11132" Priority="2" Type="Secondary">Topological Groups, Lie Groups</BookSubject>
<BookSubject Code="SCM12007" Priority="3" Type="Secondary">Analysis</BookSubject>
<BookSubject Code="SCM21022" Priority="4" Type="Secondary">Differential Geometry</BookSubject>
<BookSubject Code="SCM11000" Priority="5" Type="Secondary">Algebra</BookSubject>
<BookSubject Code="SCM25001" Priority="6" Type="Secondary">Number Theory</BookSubject>
<SubjectCollection Code="SUCO11649">Mathematics and Statistics</SubjectCollection>
</BookSubjectGroup>
</BookInfo>
<BookHeader><EditorGroup><Editor AffiliationIDS="AffID1"><EditorName DisplayOrder="Western"><GivenName>Bernhard</GivenName>
<FamilyName>Krötz</FamilyName>
</EditorName>
<Contact><Phone>0049 511 762 2361</Phone>
<Email>kroetz@math.uni-hannover.de</Email>
</Contact>
</Editor>
<Editor AffiliationIDS="AffID2"><EditorName DisplayOrder="Western"><GivenName>Omer</GivenName>
<FamilyName>Offen</FamilyName>
</EditorName>
<Contact><Phone>+49 30 2093 1806</Phone>
<Email>offen@tx.technion.ac.il</Email>
</Contact>
</Editor>
<Editor AffiliationIDS="AffID3"><EditorName DisplayOrder="Western"><GivenName>Eitan</GivenName>
<FamilyName>Sayag</FamilyName>
</EditorName>
<Contact><Phone>972-8-646-1608</Phone>
<Fax>972-8-647-7648</Fax>
<Email>sayage@math.bgu.ac.il</Email>
</Contact>
</Editor>
<Affiliation ID="AffID1"><OrgDivision>, Institut für Analysis</OrgDivision>
<OrgName>Leibniz Universität Hannover</OrgName>
<OrgAddress><Street>Welfengarten 1</Street>
<City>Hannover</City>
<Postcode>30167</Postcode>
<Country>Germany</Country>
</OrgAddress>
</Affiliation>
<Affiliation ID="AffID2"><OrgDivision>, Department of Mathematics</OrgDivision>
<OrgName>Technion-Israel Institute of Technology</OrgName>
<OrgAddress><City>Haifa</City>
<Postcode>3200</Postcode>
<Country>Israel</Country>
</OrgAddress>
</Affiliation>
<Affiliation ID="AffID3"><OrgDivision>, Department of Mathematics</OrgDivision>
<OrgName>Ben-Gurion University of the Negev</OrgName>
<OrgAddress><City>Be'er Sheva</City>
<Postcode>84105</Postcode>
<Country>Israel</Country>
</OrgAddress>
</Affiliation>
</EditorGroup>
</BookHeader>
<Chapter ID="b978-0-8176-4817-6_6" Language="En" OutputMedium="All"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" Language="En" NumberingDepth="1" NumberingStyle="ContentOnly" OutputMedium="All" TocLevels="0"><ChapterID>6</ChapterID>
<ChapterDOI>10.1007/978-0-8176-4817-6_6</ChapterDOI>
<ChapterSequenceNumber>6</ChapterSequenceNumber>
<ChapterTitle Language="En">Lectures on Lie Algebras</ChapterTitle>
<ChapterFirstPage>97</ChapterFirstPage>
<ChapterLastPage>132</ChapterLastPage>
<ChapterCopyright><CopyrightHolderName>Springer Science+Business Media, LLC</CopyrightHolderName>
<CopyrightYear>2012</CopyrightYear>
</ChapterCopyright>
<ChapterHistory><RegistrationDate><Year>2011</Year>
<Month>8</Month>
<Day>10</Day>
</RegistrationDate>
<OnlineDate><Year>2011</Year>
<Month>11</Month>
<Day>7</Day>
</OnlineDate>
</ChapterHistory>
<ChapterContext><BookID>978-0-8176-4817-6</BookID>
<BookTitle>Representation Theory, Complex Analysis, and Integral Geometry</BookTitle>
</ChapterContext>
</ChapterInfo>
<ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1_6" CorrespondingAffiliationID="Aff1_6"><AuthorName DisplayOrder="Western"><GivenName>Joseph</GivenName>
<FamilyName>Bernstein</FamilyName>
</AuthorName>
<Contact><Email>bernstei@math.tau.ac.il</Email>
</Contact>
</Author>
<Affiliation ID="Aff1_6"><OrgDivision>Department of Mathematics</OrgDivision>
<OrgName>Tel-Aviv University</OrgName>
<OrgAddress><City>Tel-Aviv</City>
<Country>Israel</Country>
</OrgAddress>
</Affiliation>
</AuthorGroup>
<Abstract ID="Abs1_6" Language="En" OutputMedium="All"><Heading>Abstract</Heading>
<Para>This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.</Para>
</Abstract>
<KeywordGroup Language="En" OutputMedium="All"><Heading>Keywords</Heading>
<Keyword>Lie algebra</Keyword>
<Keyword>Verma module</Keyword>
<Keyword>Weyl character formula</Keyword>
<Keyword>Kostant multiplicity formula</Keyword>
<Keyword>Harish–Chandra center</Keyword>
</KeywordGroup>
<ArticleNote Type="Misc"><SimplePara><Emphasis Type="Bold">1991 Mathematics Subject Classification.</Emphasis>
17A70 (Primary) 17B35 (Secondary)</SimplePara>
</ArticleNote>
</ChapterHeader>
<NoBody></NoBody>
</Chapter>
</Book>
</Publisher>
</istex:document>
</istex:metadataXml>
<mods version="3.6"><titleInfo lang="en"><title>Lectures on Lie Algebras</title>
</titleInfo>
<titleInfo type="alternative" contentType="CDATA" lang="en"><title>Lectures on Lie Algebras</title>
</titleInfo>
<name type="personal" displayLabel="corresp"><namePart type="given">Joseph</namePart>
<namePart type="family">Bernstein</namePart>
<affiliation>Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel</affiliation>
<affiliation>E-mail: bernstei@math.tau.ac.il</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Bernhard</namePart>
<namePart type="family">Krötz</namePart>
<affiliation>, Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany</affiliation>
<affiliation>E-mail: kroetz@math.uni-hannover.de</affiliation>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Omer</namePart>
<namePart type="family">Offen</namePart>
<affiliation>, Department of Mathematics, Technion-Israel Institute of Technology, 3200, Haifa, Israel</affiliation>
<affiliation>E-mail: offen@tx.technion.ac.il</affiliation>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Eitan</namePart>
<namePart type="family">Sayag</namePart>
<affiliation>, Department of Mathematics, Ben-Gurion University of the Negev, 84105, Be'er Sheva, Israel</affiliation>
<affiliation>E-mail: sayage@math.bgu.ac.il</affiliation>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="chapter" displayLabel="chapter" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-CGT4WMJM-6"></genre>
<originInfo><publisher>Birkhäuser Boston</publisher>
<place><placeTerm type="text">Boston</placeTerm>
</place>
<dateIssued encoding="w3cdtf">2011-11-07</dateIssued>
<copyrightDate encoding="w3cdtf">2012</copyrightDate>
</originInfo>
<language><languageTerm type="code" authority="rfc3066">en</languageTerm>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
</language>
<abstract lang="en">Abstract: This is a lecture course for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations (Verma modules) to derive the Weyl character formula. We also provide a proof for Harish–Chandra’s theorem on the center of the universal enveloping algebra and for Kostant’s multiplicity formula.</abstract>
<relatedItem type="host"><titleInfo><title>Representation Theory, Complex Analysis, and Integral Geometry</title>
</titleInfo>
<name type="personal"><namePart type="given">Bernhard</namePart>
<namePart type="family">Krötz</namePart>
<affiliation>, Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany</affiliation>
<affiliation>E-mail: kroetz@math.uni-hannover.de</affiliation>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Omer</namePart>
<namePart type="family">Offen</namePart>
<affiliation>, Department of Mathematics, Technion-Israel Institute of Technology, 3200, Haifa, Israel</affiliation>
<affiliation>E-mail: offen@tx.technion.ac.il</affiliation>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Eitan</namePart>
<namePart type="family">Sayag</namePart>
<affiliation>, Department of Mathematics, Ben-Gurion University of the Negev, 84105, Be'er Sheva, Israel</affiliation>
<affiliation>E-mail: sayage@math.bgu.ac.il</affiliation>
<role><roleTerm type="text">editor</roleTerm>
</role>
</name>
<genre type="book" displayLabel="Contributed volume" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-5WTPMB5N-F">book</genre>
<originInfo><publisher>Springer</publisher>
<copyrightDate encoding="w3cdtf">2012</copyrightDate>
<issuance>monographic</issuance>
</originInfo>
<subject><genre>Book-Subject-Collection</genre>
<topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic>
</subject>
<subject><genre>Book-Subject-Group</genre>
<topic authority="SpringerSubjectCodes" authorityURI="SCM">Mathematics</topic>
<topic authority="SpringerSubjectCodes" authorityURI="SCM11078">Group Theory and Generalizations</topic>
<topic authority="SpringerSubjectCodes" authorityURI="SCM11132">Topological Groups, Lie Groups</topic>
<topic authority="SpringerSubjectCodes" authorityURI="SCM12007">Analysis</topic>
<topic authority="SpringerSubjectCodes" authorityURI="SCM21022">Differential Geometry</topic>
<topic authority="SpringerSubjectCodes" authorityURI="SCM11000">Algebra</topic>
<topic authority="SpringerSubjectCodes" authorityURI="SCM25001">Number Theory</topic>
</subject>
<identifier type="DOI">10.1007/978-0-8176-4817-6</identifier>
<identifier type="ISBN">978-0-8176-4816-9</identifier>
<identifier type="eISBN">978-0-8176-4817-6</identifier>
<identifier type="BookTitleID">159517</identifier>
<identifier type="BookID">978-0-8176-4817-6</identifier>
<identifier type="BookChapterCount">10</identifier>
<part><date>2012</date>
<extent unit="pages"><start>97</start>
<end>132</end>
</extent>
</part>
<recordInfo><recordOrigin>Springer Science+Business Media, LLC, 2012</recordOrigin>
</recordInfo>
</relatedItem>
<identifier type="istex">9EE251B78CD16DD2DAD8A63F7EBF2669D0695470</identifier>
<identifier type="ark">ark:/67375/HCB-9MDS7LTZ-D</identifier>
<identifier type="DOI">10.1007/978-0-8176-4817-6_6</identifier>
<identifier type="ChapterID">6</identifier>
<identifier type="ChapterID">b978-0-8176-4817-6_6</identifier>
<accessCondition type="use and reproduction" contentType="copyright">Springer Science+Business Media, LLC, 2012</accessCondition>
<recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource>
<recordOrigin>Springer Science+Business Media, LLC, 2012</recordOrigin>
</recordInfo>
</mods>
<json:item><extension>json</extension>
<original>false</original>
<mimetype>application/json</mimetype>
<uri>https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/metadata/json</uri>
</json:item>
</metadata>
<annexes><json:item><extension>txt</extension>
<original>true</original>
<mimetype>text/plain</mimetype>
<uri>https://api.istex.fr/document/9EE251B78CD16DD2DAD8A63F7EBF2669D0695470/annexes/txt</uri>
</json:item>
</annexes>
<serie></serie>
</istex>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002050 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 002050 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Istex |étape= Corpus |type= RBID |clé= ISTEX:9EE251B78CD16DD2DAD8A63F7EBF2669D0695470 |texte= Lectures on Lie Algebras }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |