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

Author: Peter Littelmann
Journal: J. Amer. Math. Soc. 11 (1998), 551-567
MSC (1991): Primary 17B10, 17B67, 20G05, 14M15
MathSciNet review: 1603862
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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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Peter Littelmann
Affiliation: Université Louis Pasteur et Institut Universitaire de France, Institut de Recherche Mathématique Avancée 7, rue René Descartes, F-67084 Strasbourg Cedex, France

Keywords: Path model, quantum Frobenius map, standard monomial theory
Received by editor(s): July 17, 1997
Article copyright: © Copyright 1998 American Mathematical Society