Weyl group actions on the Springer sheaf
Representation Theory
2014-06-18 v2
Abstract
We show that two Weyl group actions on the Springer sheaf with arbitrary coefficients, one defined by Fourier transform and one by restriction, agree up to a twist by the sign character. This generalizes a familiar result from the setting of l-adic cohomology, making it applicable to modular representation theory. We use the Weyl group actions to define a Springer correspondence in this generality, and identify the zero weight spaces of small representations in terms of this Springer correspondence.
Cite
@article{arxiv.1304.2642,
title = {Weyl group actions on the Springer sheaf},
author = {Pramod N. Achar and Anthony Henderson and Daniel Juteau and Simon Riche},
journal= {arXiv preprint arXiv:1304.2642},
year = {2014}
}
Comments
27 pages; version 2: accepted version, with minor changes recommended by referee