Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras

Littelmann, Peter

doi:10.1090/S0894-0347-98-00268-9

Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras
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by Peter Littelmann

J. Amer. Math. Soc. 11 (1998), 551-567

DOI: https://doi.org/10.1090/S0894-0347-98-00268-9

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Abstract:

The aim of this article is to attach to the set of L-S paths of type $\lambda$ in a canonical way a basis of the corresponding representation $V(\lambda )$. This basis has some nice algebraic-geometric properties. For example, it is compatible with restrictions to Schubert varieties and has the “standard monomial property”. As a consequence we get new simple proofs of the normality of Schubert varieties, the surjectivity of the multiplication map or the restriction map for sections of a line bundle on Schubert varieties. Other applications to the defining ideal of Schubert varieties and associated Groebner basis will be discussed in a forthcoming paper.

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