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Opérateurs et polynômes de Demazure pour les algèbres de Kac-Moody finies et affines

Abstract : The aim of this work is to study Demazure modules for finite and affine type Kac-Moody algebras, and especially sl^(n). We study the character and the dimension of Demazure modules. This leads us to deal with Demazure operators, related to characters and with Demazure polynomials, related to dimension. We first show various harmonicity results for Demazure polynomials. Then, for finite type Kac-Moody algebras, we prove that the Demazure operators form a basis of the set of Z[P]^W-endomorphismes of Z[P], and that the Demazure polynomials form a basis of the set of W-harmonic polynomial that takes integer values on P. Lastly, for sl^(n), we define and study a subset E of W of nonnull density, on which we calculate the real character of Demazure module and Demazure polynomial. In small rank we deduce the polynomials on a larger subset.
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https://tel.archives-ouvertes.fr/tel-00006382
Contributor : Severine Verneyre-Petitgirard <>
Submitted on : Tuesday, July 6, 2004 - 10:37:41 AM
Last modification on : Tuesday, November 19, 2019 - 2:37:20 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 4:30:32 PM

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Séverine Verneyre-Petitgirard. Opérateurs et polynômes de Demazure pour les algèbres de Kac-Moody finies et affines. Mathématiques [math]. Université Claude Bernard - Lyon I, 2004. Français. ⟨tel-00006382⟩

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