arXiv subjects
Publications and source records attributed to Kunda Kambaso.
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.
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.