Geodesic
Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras
Littelmann, Peter 1
1 Université Louis Pasteur et Institut Universitaire de France, Institut de Recherche Mathématique Avancée 7, rue René Descartes, F-67084 Strasbourg Cedex, France
Journal of the American Mathematical Society, Tome 11 (1998) no. 3, pp. 551-567 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S0894-0347-98-00268-9

Littelmann, Peter  1

1 Université Louis Pasteur et Institut Universitaire de France, Institut de Recherche Mathématique Avancée 7, rue René Descartes, F-67084 Strasbourg Cedex, France 
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Littelmann, Peter. Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras. Journal of the American Mathematical Society, Tome 11 (1998) no. 3, pp. 551-567. doi: 10.1090/S0894-0347-98-00268-9

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