PBW filtration and monomial bases for Demazure modules in types A and C

TL;DR

This paper characterizes specific symplectic Weyl group elements for which the FFLV basis aligns with the PBW filtration on symplectic Demazure modules, revealing a rank-dependent pattern across types A and C.

Contribution

It extends type A results to type C, identifying the Weyl group elements that preserve the FFLV basis compatibility with the PBW filtration, depending only on the rank.

Findings

The number of compatible Weyl group elements depends solely on the rank.

The results unify type A and C cases through a rank-based characterization.

Extension of previous type A results to symplectic type C modules.

Abstract

We characterise the symplectic Weyl group elements such that the FFLV basis is compatible with the PBW filtration on symplectic Demazure modules, extending type A results by the second author. Surprisingly, the number of such elements depends not on the type A or C of the Lie algebra but on the rank only.