On local lifts from G2(ℝ) to Sp6(ℝ) and F4(ℝ)
Identifieur interne : 002499 ( Istex/Corpus ); précédent : 002498; suivant : 002500On local lifts from G2(ℝ) to Sp6(ℝ) and F4(ℝ)
Auteurs : Hung Yean Loke ; Gordan SavinSource :
- Israel Journal of Mathematics [ 0021-2172 ] ; 2007-06-01.
Abstract
Abstract: Let G2(ℝ) × Sp6(ℝ) and G2(ℝ) × F4(ℝ) be split dual pairs in split E7(ℝ) and E8(ℝ), respectively. It is known that the exceptional correspondences for these dual pairs are functorial on the level of infinitesimal characters. In this paper we show that these dual pair correspondences are functorial for the minimal K-types of principal series representations.
Url:
DOI: 10.1007/s11856-007-0051-5
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J. Math.</title><idno type="pISSN">0021-2172</idno><idno type="eISSN">1565-8511</idno><idno type="journal-ID">true</idno><idno type="issue-article-count">16</idno><idno type="volume-issue-count">1</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="2007-06-01"></date><biblScope unit="volume">159</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="349">349</biblScope><biblScope unit="page" to="371">371</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2005-08-08</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Let G2(ℝ) × Sp6(ℝ) and G2(ℝ) × F4(ℝ) be split dual pairs in split E7(ℝ) and E8(ℝ), respectively. It is known that the exceptional correspondences for these dual pairs are functorial on the level of infinitesimal characters. 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Math.</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Type="Primary">Mathematics</JournalSubject><JournalSubject Type="Secondary">Mathematics, general</JournalSubject><JournalSubject Type="Secondary">Algebra</JournalSubject><JournalSubject Type="Secondary">Group Theory and Generalizations</JournalSubject><JournalSubject Type="Secondary">Analysis</JournalSubject><JournalSubject Type="Secondary">Applications of Mathematics</JournalSubject><JournalSubject Type="Secondary">Mathematical and Computational Physics</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo TocLevels="0" VolumeType="Regular"><VolumeIDStart>159</VolumeIDStart><VolumeIDEnd>159</VolumeIDEnd><VolumeIssueCount>1</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd><IssueArticleCount>16</IssueArticleCount><IssueHistory><CoverDate><Year>2007</Year><Month>6</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>The Hebrew University of Jerusalem</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></IssueCopyright></IssueInfo><Article ID="s11856-007-0051-5"><ArticleInfo ArticleType="OriginalPaper" ContainsESM="No" Language="En" NumberingStyle="Unnumbered" TocLevels="0"><ArticleID>51</ArticleID><ArticleDOI>10.1007/s11856-007-0051-5</ArticleDOI><ArticleSequenceNumber>15</ArticleSequenceNumber><ArticleTitle Language="En">On local lifts from G<Subscript>2</Subscript>(ℝ) to Sp<Subscript>6</Subscript>(ℝ) and F<Subscript>4</Subscript>(ℝ)</ArticleTitle><ArticleFirstPage>349</ArticleFirstPage><ArticleLastPage>371</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2007</Year><Month>6</Month><Day>8</Day></RegistrationDate><Received><Year>2005</Year><Month>8</Month><Day>8</Day></Received></ArticleHistory><ArticleCopyright><CopyrightHolderName>The Hebrew University of Jerusalem</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></ArticleCopyright><ArticleGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ArticleGrants></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Hung</GivenName><GivenName>Yean</GivenName><FamilyName>Loke</FamilyName></AuthorName><Contact><Email>matlhy@nus.edu.sg</Email></Contact></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Gordan</GivenName><FamilyName>Savin</FamilyName></AuthorName><Contact><Email>savin@math.utah.edu</Email></Contact></Author><Affiliation ID="Aff1"><OrgDivision>Department of Mathematics</OrgDivision><OrgName>National University of Singapore</OrgName><OrgAddress><Street>2 Science Drive 2</Street><City>Singapore</City><Postcode>117543</Postcode></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Department of Mathematics</OrgDivision><OrgName>University of Utah</OrgName><OrgAddress><City>Salt Lake City</City><State>UT</State><Postcode>84112</Postcode><Country Code="US">USA</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Let G<Subscript>2</Subscript>(ℝ) × Sp<Subscript>6</Subscript>(ℝ) and G<Subscript>2</Subscript>(ℝ) × F<Subscript>4</Subscript>(ℝ) be split dual pairs in split E<Subscript>7</Subscript>(ℝ) and E<Subscript>8</Subscript>(ℝ), respectively. It is known that the exceptional correspondences for these dual pairs are functorial on the level of infinitesimal characters. In this paper we show that these dual pair correspondences are functorial for the minimal <Emphasis Type="Italic">K</Emphasis>-types of principal series representations.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Gordan Savin’s research is partially supported be NSF Grant no. DMS-0551846</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On local lifts from G2(ℝ) to Sp6(ℝ) and F4(ℝ)</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>On local lifts from G2(ℝ) to Sp6(ℝ) and F4(ℝ)</title></titleInfo><name type="personal"><namePart type="given">Hung</namePart><namePart type="given">Yean</namePart><namePart type="family">Loke</namePart><affiliation>Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543, Singapore</affiliation><affiliation>E-mail: matlhy@nus.edu.sg</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Gordan</namePart><namePart type="family">Savin</namePart><affiliation>Department of Mathematics, University of Utah, 84112, Salt Lake City, UT, USA</affiliation><affiliation>E-mail: savin@math.utah.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>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">2005-08-08</dateCreated><dateIssued encoding="w3cdtf">2007-06-01</dateIssued><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: Let G2(ℝ) × Sp6(ℝ) and G2(ℝ) × F4(ℝ) be split dual pairs in split E7(ℝ) and E8(ℝ), respectively. It is known that the exceptional correspondences for these dual pairs are functorial on the level of infinitesimal characters. In this paper we show that these dual pair correspondences are functorial for the minimal K-types of principal series representations.</abstract><relatedItem type="host"><titleInfo><title>Israel Journal of Mathematics</title></titleInfo><titleInfo type="abbreviated"><title>Isr. J. 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