Exterior powers of a parabolic Springer sheaf on a Lie algebra

TL;DR

This paper computes the exterior powers of a parabolic Springer sheaf on a Lie algebra, revealing their isomorphism to semisimple perverse sheaves linked to symmetric group representations, advancing understanding in geometric representation theory.

Contribution

It provides an explicit calculation of exterior powers of a specific Springer sheaf and establishes their isomorphism to known perverse sheaves via the Springer correspondence.

Findings

Exterior powers are isomorphic to semisimple perverse sheaves.

Connection established between Springer sheaves and symmetric group representations.

Advances understanding of the structure of Springer sheaves in geometric representation theory.

Abstract

We compute the exterior powers, with respect to the additive convolution on the general linear Lie algebra, of a parabolic Springer sheaf corresponding to a maximal parabolic subgroup of type (1, n -- 1). They turn out to be isomorphic to the semisimple perverse sheaves attached by the Springer correspondence to the exterior powers of the permutation representation of the symmetric group.