A geometric Schur functor
Representation Theory
2014-02-07 v2 Algebraic Geometry
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.
Cite
@article{arxiv.1210.3635,
title = {A geometric Schur functor},
author = {Carl Mautner},
journal= {arXiv preprint arXiv:1210.3635},
year = {2014}
}
Comments
15 pages, v2 - notation made consistent and assumptions on coefficients clarified. Accepted for publication in Selecta Math