Exterior powers of a parabolic Springer sheaf on a Lie algebra

Roman Bezrukavnikov; Kostiantyn Tolmachov

Exterior powers of a parabolic Springer sheaf on a Lie algebra

Representation Theory 2024-03-29 v2 Algebraic Geometry

Authors: Roman Bezrukavnikov , Kostiantyn Tolmachov

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.

Keywords

exterior powers parabolic springer sheaf lie algebra additive convolution springer correspondence symmetric group perverse sheaves

Cite

@article{arxiv.2209.01603,
  title  = {Exterior powers of a parabolic Springer sheaf on a Lie algebra},
  author = {Roman Bezrukavnikov and Kostiantyn Tolmachov},
  journal= {arXiv preprint arXiv:2209.01603},
  year   = {2024}
}

Comments

Content reorganised. Proofs for the Lie algebra statement significantly simplified. Material related to the convolution on the group was moved to the preprint "Linear structure on a finite Hecke category in type A" by the second author

Exterior powers of a parabolic Springer sheaf on a Lie algebra

Abstract

Keywords

Cite

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