PBW-degenerated Demazure modules and Schubert varieties for triangular elements

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:139

Article

Fourier, Ghislain^1,2 

[1] Univ Bonn, Math Inst, Bonn, Germany

[2] Univ Glasgow, Sch Math & Stat, Glasgow G12 8QQ, Lanark, Scotland

关键词: Toric degeneration;    Schubert variety;    PBW filtration;    Demazure module;   

DOI  :  10.1016/j.jcta.2015.12.001

来源: Elsevier

【 摘 要 】

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 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. (C) 2015 Elsevier. Inc. All rights reserved.

【 授权许可】

Free