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arXiv · 1009.2895

Betti numbers of smooth Schubert varieties and the remarkable formula of Kostant,Macdonald,Shapiro and Steinberg

Ersan Akyildiz·James B. Carrell
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Abstract

The purpose of this note is to give a refinement of the product formula proved in [1] for the Poincare polynomial of a smooth Schubert variety in the flag variety of an algebraic group G over C. This yields a factorization of the number of elements in a Bruhat interval [e,w] in the Weyl group W of G provided the Schubert variety associated to w is smooth. This gives an elementary necessary condition for a Schubert variety in the flag variety to be smooth.

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Ersan Akyildiz, James B. Carrell. 2010-09-15. Betti numbers of smooth Schubert varieties and the remarkable formula of Kostant,Macdonald,Shapiro and Steinberg. https://arxiv.org/abs/1009.2895

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