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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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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


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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Bibliographic Information
  • 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
  • Email:
  • Received by editor(s): July 17, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 551-567
  • MSC (1991): Primary 17B10, 17B67, 20G05, 14M15
  • DOI:
  • MathSciNet review: 1603862