A geometric Schur functor

Abstract

We give geometric descriptions of the category C_k(n,d) of rational polynomial representations of GL_n over a field k of degree d for d less than or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and proofs use a modular version of Springer theory and relationships between the equivariant geometry of the affine Grassmannian and the nilpotent cone for the general linear groups. Motivated by this description, we propose generalizations for an arbitrary connected complex reductive group of the category C_k(n,d) and the Schur functor.

15 pages, v2 - notation made consistent and assumptions on coefficients clarified. Accepted for publication in Selecta Math

References in corpus (4)

• Quiver varieties and Beilinson-Drinfeld Grassmannians of type A
• Correspondance de Springer modulaire et matrices de décomposition
• Geometric Satake, Springer correspondence, and small representations II
• Modular generalized Springer correspondence I: the general linear group

Cited by in corpus (2)

• Modular Springer correspondence, decomposition matrices and basic sets
• Geometric Satake, Springer correspondence, and small representations II