PBW-degenerated Demazure modules and Schubert varieties for triangular elements

Fourier, G. (2016) PBW-degenerated Demazure modules and Schubert varieties for triangular elements. Journal of Combinatorial Theory, Series A, 139, pp. 132-152. (doi: 10.1016/j.jcta.2015.12.001)

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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 sln+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.

Item Type:Articles
Additional Information:The author is supported by the project “Shuffles and Schur positivity” within DFG priority program 1388 “Representation Theory”.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Fourier, Dr Ghislain
Authors: Fourier, G.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Combinatorial Theory, Series A
Publisher:Elsevier
ISSN:0097-3165
Published Online:15 December 2015
First Published:First published in Journal of Combinatorial Theory, Series A 139: 132-152
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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