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arXiv · 0906.4866

Gelfand-Zetlin polytopes and flag varieties

Valentina Kiritchenko
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Abstract

I construct a correspondence between the Schubert cycles on the variety of complete flags in C^n and some faces of the Gelfand-Zetlin polytope associated with the irreducible representation of SL_n(C) with a strictly dominant highest weight. The construction is based on a geometric presentation of Schubert cells by Bernstein-Gelfand-Gelfand using Demazure modules. The correspondence between the Schubert cycles and faces is then used to interpret the classical Chevalley formula in Schubert calculus in terms of the Gelfand-Zetlin polytopes. The whole picture resembles the picture for toric varieties and their polytopes.

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Valentina Kiritchenko. 2009-06-26. Gelfand-Zetlin polytopes and flag varieties. https://doi.org/10.1093/imrn%2Frnp223

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