Derived supersymmetries of determinantal varieties

Abstract

We show that the linear strands of the Tor of determinantal varieties in spaces of symmetric and skew-symmetric matrices are irreducible representations for the periplectic (strange) Lie superalgebra. The structure of these linear strands is explicitly known, so this gives an explicit realization of some representations of the periplectic Lie superalgebra. This complements results of Pragacz and Weyman, who showed an analogous statement for the generic determinantal varieties and the general linear Lie superalgebra. We also give a simpler proof of their result. Via Koszul duality, this is an odd analogue of the fact that the coordinate rings of these determinantal varieties are irreducible representations for a certain classical Lie algebra.

17 pages

References in corpus (1)

• Schubert complexes and degeneracy loci

Cited by in corpus (5)

• Homological invariants of determinantal thickenings
• Syzygies of determinantal thickenings and representations of the general linear Lie superalgebra
• Equivariant resolutions over Veronese rings
• Conjectures and computations about Veronese syzygies
• Cohomology of flag supervarieties and resolutions of determinantal ideals