2026/07/13 by Ibrahim Ahmad, Pranav Enugandla
#math.RT #math.CO
We study the PBW filtration on covariant representations for the Lie superalgebra \mathfrakgl(m|n). We prove for all covariant weights of the form (λ|μ,0n-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.