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Formules de caractères pour les algèbres de Kac-Moody générales / Olivier Mathieu

Auteur principal : Mathieu, Olivier, 1960-, AuteurType de document : MonographieCollection : Astérisque, 159-160Langue : français.Pays : France.Éditeur : Paris : Société Mathématique de France, 1988Description : 1 vol. (267 p.) : ill. ; 24 cmISSN : 0303-1179.Bibliographie : Bibliogr. p. 262-266.Sujet MSC : 17B67, Nonassociative rings and algebras -- Lie algebras and Lie superalgebras, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B10, Nonassociative rings and algebras -- Lie algebras and Lie superalgebras, Representations, algebraic theory (weights)
14M15, Algebraic geometry -- Special varieties, Grassmannians, Schubert varieties, flag manifolds
17B65, Nonassociative rings and algebras -- Lie algebras and Lie superalgebras, Infinite-dimensional Lie (super)algebras
14Fxx, Algebraic geometry, (Co)homology theory
En-ligne : Numdam
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Séries SMF 159/160 (Browse shelf) Available 09667-01

The author extends Demazure's character formula to any Kac-Moody algebra (not necessarily symmetrizable). From this, using an argument of G. Heckman, he gets the Weyl character formula. Underlying these results, there is the identification of the characters with some Euler-Poincaré characteristic dimensions and the proof of vanishing theorems for the cohomology of semi-ample line bundles over the Schubert varieties. This machinery also allows him to prove a generalization of the Bott-Borel- Weyl theorem and Kempf's theorem, as well as some properties of the Schubert varieties. (Zentralblatt)

Bibliogr. p. 262-266

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