FFLV bases for covariant representations of $\mathfrak{gl}(m|n)$

Abstract

We study the PBW filtration on covariant representations for the Lie superalgebra $\mathfrak{gl}(m|n)$. We prove for all covariant weights of the form $(\lambda |\mu ,0^{n-1})$, that there exists a lattice polytope such that the lattice points of this polytope parametrize a basis of the corresponding associated graded space. As a consequence, we obtain degenerations of partial flag supervarieties for the supergroup $GL(m|n)$ into toric supervarieties.

23 pages. Proposition 3.7 and Section 6 revised