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- W1928961937 abstract "The aim of this article is to attach to the set of L-S paths of type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=lamda> <mml:semantics> <mml:mi>λ<!-- λ --></mml:mi> <mml:annotation encoding=application/x-tex>lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a canonical way a basis of the corresponding representation <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper V left-parenthesis lamda right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>λ<!-- λ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>V(lambda )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. 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." @default.
- W1928961937 created "2016-06-24" @default.
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- W1928961937 date "1998-01-01" @default.
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- W1928961937 title "Contracting modules and standard monomial theory for symmetrizable Kac-Moody algebras" @default.
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- W1928961937 doi "https://doi.org/10.1090/s0894-0347-98-00268-9" @default.
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