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