Mathematics – Algebraic Geometry
Scientific paper
2009-06-26
International Mathematics Research Notices (2009), 20 pages, doi:10.1093/imrn/rnp223
Mathematics
Algebraic Geometry
16 pages, 2 figures
Scientific paper
10.1093/imrn/rnp223
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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