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.
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DOI: 10.1007/978-0-8176-4817-6_6
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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. 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