Betti Numbers of Smooth Schubert Varieties and the Remarkable Formula of Kostant, Macdonald, Shapiro, and Steinberg

Date

2012-01-01

Author

Akyıldız, Ersan

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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.

Subject Keywords

Mathematics

URI

https://hdl.handle.net/11511/54745

Journal

MICHIGAN MATHEMATICAL JOURNAL

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Graduate School of Applied Mathematics, Article

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Citation Formats

E. Akyıldız, “Betti Numbers of Smooth Schubert Varieties and the Remarkable Formula of Kostant, Macdonald, Shapiro, and Steinberg,” MICHIGAN MATHEMATICAL JOURNAL, pp. 543–553, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54745.