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arXiv · 2007.11054

Homogeneous Bases for Demazure Modules

Kunda Kambaso
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Abstract

We study the PBW filtration on the Demazure modules $V_{r_γ}(λ)$ associated to reflections $r_γ$ at positive roots in type $A_n$, long roots in type $C_n$, short roots in type $B_n$ and positive roots not involving the simple root $α_{n-1}$ in type $D_n$. In each type, we construct a normal polytope labelling a basis for the associated graded space $\operatorname{gr} V_{r_γ}(λ)$ and prove that the annihilating ideal of $\operatorname{gr} V_{r_γ}(λ)$ is a monomial ideal.

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Kunda Kambaso. 2021-05-18. Homogeneous Bases for Demazure Modules. https://arxiv.org/abs/2007.11054

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