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Representations of quantum groups at a p-TH root of unity and of semisimple groups in characteristic p : independance of p / H. H ANDERSEN (1994)
Titre : Representations of quantum groups at a p-TH root of unity and of semisimple groups in characteristic p : independance of p Type de document : texte imprimé Auteurs : H. H ANDERSEN, Auteur ; J.C JANTZEN, Auteur ; SOERGEL, Auteur Editeur : Paris : Société Mathématique de France Année de publication : 1994 Collection : Astérisque, ISSN 0303-1179 num. 220 Importance : 321 p. Langues : Anglais Catégories : 17B35
17B37
20G05Résumé : Consider an indecomposable finite root system R. associate to R two families of objects :
1.) For any odd integer p>1 (prime to 3 if R is of type G2) let Up be the quantized enveloping algebra at a p-th root of unity. We take here Lusztig's version.
2.) For any prime p let Gp be the semisimple connected and simply connected algebraic group over an algebraically closed field of characteristic p.
Restrict to the case where p is greater than the Coxeter number h of R. Consider the block of the trivial one dimensional module for Up resp. for Gp. The simple modules in this block are indexed by certain elements in the affine Weyl group Wa of R. Suppose that Lw is the simple module indexed by w and that Vw is the Weyl module with head Lw. We show that there are integers dw,x independent of p such that in the Up case (resp. in the Gp case) dw,x is equal to the multiplicity of Lx as a composition factor of Vw for all p>h (resp. for all p>>0). This implies : If the Lusztig conjecture holds in the quantum case, then it holds for p>>0 in the prime characteristic caseNote de contenu : notations, références Representations of quantum groups at a p-TH root of unity and of semisimple groups in characteristic p : independance of p [texte imprimé] / H. H ANDERSEN, Auteur ; J.C JANTZEN, Auteur ; SOERGEL, Auteur . - Paris : Société Mathématique de France, 1994 . - 321 p.. - (Astérisque, ISSN 0303-1179; 220) .
Langues : Anglais
Catégories : 17B35
17B37
20G05Résumé : Consider an indecomposable finite root system R. associate to R two families of objects :
1.) For any odd integer p>1 (prime to 3 if R is of type G2) let Up be the quantized enveloping algebra at a p-th root of unity. We take here Lusztig's version.
2.) For any prime p let Gp be the semisimple connected and simply connected algebraic group over an algebraically closed field of characteristic p.
Restrict to the case where p is greater than the Coxeter number h of R. Consider the block of the trivial one dimensional module for Up resp. for Gp. The simple modules in this block are indexed by certain elements in the affine Weyl group Wa of R. Suppose that Lw is the simple module indexed by w and that Vw is the Weyl module with head Lw. We show that there are integers dw,x independent of p such that in the Up case (resp. in the Gp case) dw,x is equal to the multiplicity of Lx as a composition factor of Vw for all p>h (resp. for all p>>0). This implies : If the Lusztig conjecture holds in the quantum case, then it holds for p>>0 in the prime characteristic caseNote de contenu : notations, références Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 15980 AST220 Livre Recherche Salle Disponible Squared hopf algebras / Volodymyr V. LYUBASHENKO (1999)
Titre : Squared hopf algebras Type de document : monographie Auteurs : Volodymyr V. LYUBASHENKO, Auteur Editeur : Providence, R. I. [Etats Unis] : American Mathematical Society Année de publication : 1999 Collection : Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 677 ISBN/ISSN/EAN : 978-0-8218-1361-4 Note générale : Bibliogr. Langues : Anglais Catégories : 16D90
16W30
17B37
18D10
18D15
18D20Mots-clés : coalgèbre Hopf Squared hopf algebras [monographie] / Volodymyr V. LYUBASHENKO, Auteur . - Providence, R. I. (Etats Unis) : American Mathematical Society, 1999. - (Memoirs of the American Mathematical Society, ISSN 0065-9266; 677) .
ISBN : 978-0-8218-1361-4
Bibliogr.
Langues : Anglais
Catégories : 16D90
16W30
17B37
18D10
18D15
18D20Mots-clés : coalgèbre Hopf Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 16781 854/677 Livre Recherche Salle Disponible The interplay between differential geometry and differential equations / V. V. LYCHAGIN (Cop. 1995)
Titre : The interplay between differential geometry and differential equations Type de document : texte imprimé Auteurs : V. V. LYCHAGIN, Editeur scientifique Editeur : Providence, R. I. [Etats Unis] : American Mathematical Society Année de publication : Cop. 1995 Collection : American Mathematical Society Translations. Series 2, ISSN 0065-9290 num. 167 Importance : IX-294 p. ISBN/ISSN/EAN : 978-0-8218-0428-5 Langues : Anglais Langues originales : Russe Catégories : 17B37
35Axx
58Axx
58GxxMots-clés : équation différentielle géométrie différentielle Résumé : A collection that presents work concentrated mainly around the differential geometry approach to the theory of nonlinear differential equations. The papers can be subdivided into three groups: general questions of the geometric theory of differential equations and the methods of differential geometry used in their study; applications of the geometric theory of differential equations to the study of specific problems; and quantization problems. Note de contenu : références The interplay between differential geometry and differential equations [texte imprimé] / V. V. LYCHAGIN, Editeur scientifique . - Providence, R. I. (Etats Unis) : American Mathematical Society, Cop. 1995 . - IX-294 p.. - (American Mathematical Society Translations. Series 2, ISSN 0065-9290; 167) .
ISBN : 978-0-8218-0428-5
Langues : Anglais Langues originales : Russe
Catégories : 17B37
35Axx
58Axx
58GxxMots-clés : équation différentielle géométrie différentielle Résumé : A collection that presents work concentrated mainly around the differential geometry approach to the theory of nonlinear differential equations. The papers can be subdivided into three groups: general questions of the geometric theory of differential equations and the methods of differential geometry used in their study; applications of the geometric theory of differential equations to the study of specific problems; and quantization problems. Note de contenu : références Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 8221 858/167 Livre Recherche Salle Disponible