Weyl group actions on the Springer sheaf
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. © 2013 London Mathematical Society.
Publication Source (Journal or Book title)
Proceedings of the London Mathematical Society
Achar, P., Henderson, A., Juteau, D., & Riche, S. (2014). Weyl group actions on the Springer sheaf. Proceedings of the London Mathematical Society, 108 (6), 1501-1528. https://doi.org/10.1112/plms/pdt055