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, Lie algebras and Lie superalgebras, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B10, Lie algebras and Lie superalgebras, Representations, algebraic theory (weights)
14M15, Algebraic geometry - Special varieties, Grassmannians, Schubert varieties, flag manifolds
17B65, Lie algebras and Lie superalgebras, Infinite-dimensional
14Fxx, Algebraic geometry - (Co)homology theory in algebraic geometry
En-ligne : Numdam
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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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