Sur les semi-invariants d'une sous-algèbre parabolique d'une algèbre enveloppante quantifiée
Identifieur interne : 001178 ( Main/Merge ); précédent : 001177; suivant : 001179Sur les semi-invariants d'une sous-algèbre parabolique d'une algèbre enveloppante quantifiée
Auteurs : F. Fauquant-Millet [France] ; A. Joseph [France, Israël]Source :
- Transformation Groups [ 1083-4362 ] ; 2001-06-01.
Abstract
Abstract: Let Ŭ q (g π) be the simply connected quantized enveloping algebra of the complex semisimple finite dimensional Lie algebrag π. Letp be a parabolic subalgebra ofg π and $$\mathcal{P}: = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{U} _q \left( {g_\pi } \right)$$ the Hopf subalgebra of Ŭ q (g π) associated top. LetY $$\left( \mathcal{P} \right)$$ be the space generated by the semi-invariants of $$\mathcal{P}$$ under adjoint action. We describe a basis forY $$\left( \mathcal{P} \right)$$ , show that it is a polynomial algebra and describe its rank, which we compute explicitly in a number of cases. Except for the Borel and some special cases a corresponding result is not known for the semi-centre of the enveloping algebra ofp. However we show here that the latter has the same Gelfand-Kirillov dimension asY $$\left( \mathcal{P} \right)$$ . We also describe the multiplication rules of the above basos elements ofY $$\left( \mathcal{P} \right)$$ . These are analogous to “fusion rules” in tensor product decomposition and their derivation obtains from an analysis of theR-matrix.
Url:
DOI: 10.1007/BF01597132
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="fr">Sur les semi-invariants d'une sous-algèbre parabolique d'une algèbre enveloppante quantifiée</title><author><name sortKey="Fauquant Millet, F" sort="Fauquant Millet, F" uniqKey="Fauquant Millet F" first="F." last="Fauquant-Millet">F. Fauquant-Millet</name></author><author><name sortKey="Joseph, A" sort="Joseph, A" uniqKey="Joseph A" first="A." last="Joseph">A. Joseph</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:EFA076C2B387FCEE90C3557897BEA563846B06EA</idno><date when="2001" year="2001">2001</date><idno type="doi">10.1007/BF01597132</idno><idno type="url">https://api.istex.fr/document/EFA076C2B387FCEE90C3557897BEA563846B06EA/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">003115</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">003115</idno><idno type="wicri:Area/Istex/Curation">003115</idno><idno type="wicri:Area/Istex/Checkpoint">001039</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001039</idno><idno type="wicri:doubleKey">1083-4362:2001:Fauquant Millet F:sur:les:semi</idno><idno type="wicri:Area/Main/Merge">001178</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="fr">Sur les semi-invariants d'une sous-algèbre parabolique d'une algèbre enveloppante quantifiée</title><author><name sortKey="Fauquant Millet, F" sort="Fauquant Millet, F" uniqKey="Fauquant Millet F" first="F." last="Fauquant-Millet">F. Fauquant-Millet</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Faculté des Sciences et Techniques Départment de Mathématiques, Université Jean Monnet, 23, rue du Dr Paul Michelon, 42023, Saint-Etienne Cédex 02</wicri:regionArea><placeName><region type="region" nuts="2">Auvergne-Rhône-Alpes</region><region type="old region" nuts="2">Rhône-Alpes</region><settlement type="city">Saint-Etienne Cédex 02</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Joseph, A" sort="Joseph, A" uniqKey="Joseph A" first="A." last="Joseph">A. Joseph</name><affiliation wicri:level="1"><country xml:lang="fr">France</country><wicri:regionArea>Institut de Mathémqtiques, 175, rue du Chevaleret, Plateau 7 D, 75013, Paris Cédex</wicri:regionArea><wicri:noRegion>75013, Paris Cédex</wicri:noRegion><wicri:noRegion>Paris Cédex</wicri:noRegion></affiliation><affiliation wicri:level="1"><country xml:lang="fr">Israël</country><wicri:regionArea>Department of Mathematics, The Weizmann Institute of Science, 76100, Rehovot</wicri:regionArea><wicri:noRegion>Rehovot</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Israël</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Transformation Groups</title><title level="j" type="abbrev">Transformation Groups</title><idno type="ISSN">1083-4362</idno><idno type="eISSN">1531-586X</idno><imprint><publisher>Birkhäuser-Verlag</publisher><pubPlace>Boston</pubPlace><date type="published" when="2001-06-01">2001-06-01</date><biblScope unit="volume">6</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="125">125</biblScope><biblScope unit="page" to="142">142</biblScope></imprint><idno type="ISSN">1083-4362</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">1083-4362</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="fr">fr</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Let Ŭ q (g π) be the simply connected quantized enveloping algebra of the complex semisimple finite dimensional Lie algebrag π. Letp be a parabolic subalgebra ofg π and $$\mathcal{P}: = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{U} _q \left( {g_\pi } \right)$$ the Hopf subalgebra of Ŭ q (g π) associated top. LetY $$\left( \mathcal{P} \right)$$ be the space generated by the semi-invariants of $$\mathcal{P}$$ under adjoint action. We describe a basis forY $$\left( \mathcal{P} \right)$$ , show that it is a polynomial algebra and describe its rank, which we compute explicitly in a number of cases. Except for the Borel and some special cases a corresponding result is not known for the semi-centre of the enveloping algebra ofp. However we show here that the latter has the same Gelfand-Kirillov dimension asY $$\left( \mathcal{P} \right)$$ . We also describe the multiplication rules of the above basos elements ofY $$\left( \mathcal{P} \right)$$ . These are analogous to “fusion rules” in tensor product decomposition and their derivation obtains from an analysis of theR-matrix.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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