New Directions in Representation Theory
Identifieur interne : 001609 ( Istex/Corpus ); précédent : 001608; suivant : 001610New Directions in Representation Theory
Auteurs : Charles W. CurtisSource :
- Milan Journal of Mathematics [ 1424-9286 ] ; 2012-06-01.
Abstract
Abstract: The Iwahori–Hecke algebra H(G, B) of a finite Chevalley group G with respect to a Borel subgroup B is described as a deformation of the group algebra of the Weyl group of G Similarly, the +-part of the quantized enveloping algebra $${{U^+_v (\mathfrak{g})}}$$ associated with a semisimple Lie algebra $${{\mathfrak{g}}}$$ can be viewed as a deformation of the +-part of the universal enveloping algebra $${{U(\mathfrak{g})}}$$ . In both cases it is shown how information concerning the deformed algebras H(G, B) and $${{U^+_v (\mathfrak{g})}}$$ can be used to obtain results about the representation theory of the Chevalley group G and the semisimple Lie algebra $${{\mathfrak{g}}}$$ .
Url:
DOI: 10.1007/s00032-012-0177-8
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Curtis</name><affiliation><mods:affiliation>Department of Mathematics, University of Oregon, 97403, Eugene, Oregon, USA</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: cwc@uoregon.edu</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Milan Journal of Mathematics</title><title level="j" type="sub">Issued by the Seminario Matematico e Fisico di Milano</title><title level="j" type="abbrev">Milan J. Math.</title><idno type="ISSN">1424-9286</idno><idno type="eISSN">1424-9294</idno><imprint><publisher>SP Birkhäuser Verlag Basel</publisher><pubPlace>Basel</pubPlace><date type="published" when="2012-06-01">2012-06-01</date><biblScope unit="volume">80</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="151">151</biblScope><biblScope unit="page" to="167">167</biblScope></imprint><idno type="ISSN">1424-9286</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1424-9286</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The Iwahori–Hecke algebra H(G, B) of a finite Chevalley group G with respect to a Borel subgroup B is described as a deformation of the group algebra of the Weyl group of G Similarly, the +-part of the quantized enveloping algebra $${{U^+_v (\mathfrak{g})}}$$ associated with a semisimple Lie algebra $${{\mathfrak{g}}}$$ can be viewed as a deformation of the +-part of the universal enveloping algebra $${{U(\mathfrak{g})}}$$ . In both cases it is shown how information concerning the deformed algebras H(G, B) and $${{U^+_v (\mathfrak{g})}}$$ can be used to obtain results about the representation theory of the Chevalley group G and the semisimple Lie algebra $${{\mathfrak{g}}}$$ .</div></front></TEI><istex><corpusName>springer-journals</corpusName><author><json:item><name>Charles W. 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In both cases it is shown how information concerning the deformed algebras H(G, B) and $${{U^+_v (\mathfrak{g})}}$$ can be used to obtain results about the representation theory of the Chevalley group G and the semisimple Lie algebra $${{\mathfrak{g}}}$$ .</abstract><qualityIndicators><score>8.272</score><pdfWordCount>7565</pdfWordCount><pdfCharCount>34761</pdfCharCount><pdfVersion>1.4</pdfVersion><pdfPageCount>17</pdfPageCount><pdfPageSize>547.087 x 737.008 pts</pdfPageSize><refBibsNative>false</refBibsNative><abstractWordCount>106</abstractWordCount><abstractCharCount>695</abstractCharCount><keywordCount>4</keywordCount></qualityIndicators><title>New Directions in Representation Theory</title><genre><json:string>research-article</json:string></genre><host><title>Milan Journal of Mathematics</title><language><json:string>unknown</json:string></language><publicationDate>2012</publicationDate><copyrightDate>2012</copyrightDate><issn><json:string>1424-9286</json:string></issn><eissn><json:string>1424-9294</json:string></eissn><journalId><json:string>32</json:string></journalId><volume>80</volume><issue>1</issue><pages><first>151</first><last>167</last></pages><genre><json:string>journal</json:string></genre><subject><json:item><value>SC10</value></json:item><json:item><value>Analysis</value></json:item><json:item><value>Mathematics, general</value></json:item></subject></host><ark><json:string>ark:/67375/VQC-9J9NLSCS-M</json:string></ark><publicationDate>2012</publicationDate><copyrightDate>2012</copyrightDate><doi><json:string>10.1007/s00032-012-0177-8</json:string></doi><id>6BF8F4B303999CA959BF3A6DC8254E9F8DF5DF69</id><score>1</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/6BF8F4B303999CA959BF3A6DC8254E9F8DF5DF69/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/6BF8F4B303999CA959BF3A6DC8254E9F8DF5DF69/fulltext/zip</uri></json:item><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/6BF8F4B303999CA959BF3A6DC8254E9F8DF5DF69/fulltext/txt</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/6BF8F4B303999CA959BF3A6DC8254E9F8DF5DF69/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">New Directions in Representation Theory</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">SP Birkhäuser Verlag Basel</publisher><pubPlace>Basel</pubPlace><availability><licence><p>Springer Basel AG, 2012</p></licence><p scheme="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</p></availability><date>2012-01-17</date></publicationStmt><notesStmt><note type="research-article" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</note><note type="journal" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">New Directions in Representation Theory</title><author xml:id="author-0000" corresp="yes"><persName><forename type="first">Charles</forename><surname>Curtis</surname></persName><email>cwc@uoregon.edu</email><affiliation>Department of Mathematics, University of Oregon, 97403, Eugene, Oregon, USA</affiliation></author><idno type="istex">6BF8F4B303999CA959BF3A6DC8254E9F8DF5DF69</idno><idno type="ark">ark:/67375/VQC-9J9NLSCS-M</idno><idno type="DOI">10.1007/s00032-012-0177-8</idno><idno type="article-id">177</idno><idno type="article-id">s00032-012-0177-8</idno></analytic><monogr><title level="j">Milan Journal of Mathematics</title><title level="j" type="sub">Issued by the Seminario Matematico e Fisico di Milano</title><title level="j" type="abbrev">Milan J. 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In both cases it is shown how information concerning the deformed algebras <Emphasis Type="Italic">H(G, B)</Emphasis> and <InlineEquation ID="IEq4"><InlineMediaObject><ImageObject Color="BlackWhite" FileRef="32_2012_177_Article_IEq4.gif" Format="GIF" Rendition="HTML" Type="Linedraw"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$${{U^+_v (\mathfrak{g})}}$$</EquationSource></InlineEquation> can be used to obtain results about the representation theory of the Chevalley group <Emphasis Type="Italic">G</Emphasis> and the semisimple Lie algebra <InlineEquation ID="IEq5"><InlineMediaObject><ImageObject Color="BlackWhite" FileRef="32_2012_177_Article_IEq5.gif" Format="GIF" Rendition="HTML" Type="Linedraw"></ImageObject></InlineMediaObject><EquationSource Format="TEX">$${{\mathfrak{g}}}$$</EquationSource></InlineEquation> .</Para></Abstract><KeywordGroup Language="En"><Heading>Mathematics Subject Classification (2010)</Heading><Keyword>Primary 20C08</Keyword><Keyword>17B37</Keyword><Keyword>Secondary20C33</Keyword><Keyword>17B10</Keyword></KeywordGroup><KeywordGroup Language="--"><Heading>Keywords</Heading><Keyword>Chevalley groups</Keyword><Keyword>Iwahori–Hecke algebras</Keyword><Keyword>quantized enveloping algebras</Keyword><Keyword>Ringel–Hall algebras</Keyword></KeywordGroup><ArticleNote Type="CommunicatedBy"><SimplePara>Leonardo da Vinci Lecture held on October 17, 2011</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>New Directions in Representation Theory</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>New Directions in Representation Theory</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">Charles</namePart><namePart type="given">W.</namePart><namePart type="family">Curtis</namePart><affiliation>Department of Mathematics, University of Oregon, 97403, Eugene, Oregon, USA</affiliation><affiliation>E-mail: cwc@uoregon.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>SP Birkhäuser Verlag Basel</publisher><place><placeTerm type="text">Basel</placeTerm></place><dateCreated encoding="w3cdtf">2012-01-17</dateCreated><dateIssued encoding="w3cdtf">2012-06-01</dateIssued><dateIssued encoding="w3cdtf">2012</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: The Iwahori–Hecke algebra H(G, B) of a finite Chevalley group G with respect to a Borel subgroup B is described as a deformation of the group algebra of the Weyl group of G Similarly, the +-part of the quantized enveloping algebra $${{U^+_v (\mathfrak{g})}}$$ associated with a semisimple Lie algebra $${{\mathfrak{g}}}$$ can be viewed as a deformation of the +-part of the universal enveloping algebra $${{U(\mathfrak{g})}}$$ . 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