PBW-degenerated Demazure modules and Schubert varieties for triangular elements

Ghislain Fourier

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arXiv · 1408.6939

PBW-degenerated Demazure modules and Schubert varieties for triangular elements

Ghislain Fourier

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Abstract

We study certain faces of the normal polytope introduced by Feigin, Littelmann and the author whose lattice points parametrize a monomial basis of the PBW-degenerated of simple modules for $\mathfrak{sl}_{n+1}$. We show that lattice points in these faces parametrize monomial bases of PBW-degenerated Demazure modules associated to Weyl group elements satisfying a certain closure property, for example Kempf elements. These faces are again normal polytopes and their Minkowski sum is compatible with tensor products, which implies that we obtain flat degenerations of the corresponding Schubert varieties to PBW degenerated and toric varieties.

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Ghislain Fourier. 2014-08-29. PBW-degenerated Demazure modules and Schubert varieties for triangular elements. https://arxiv.org/abs/1408.6939

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