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

Ibrahim Ahmad; Pranav Enugandla

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arXiv · 2607.11133

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

Ibrahim Ahmad·Pranav Enugandla

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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.

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BibTeX RIS

Ibrahim Ahmad, Pranav Enugandla. 2026-07-13. FFLV bases for covariant representations of $\mathfrak{gl}(m|n)$. https://arxiv.org/abs/2607.11133

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