Document Type
Article
Publication Date
1-1-2015
Abstract
For a split reductive group scheme Ğ over a commutative ring K with Weyl group W, there is an important functor Rep( Ğ, K) → Rep(W; K) defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of small representations has an alternative geometric description, in terms of the affine Grassmannian and the nilpotent cone of the Langlands dual group G. The translation from representation theory to geometry is via the Satake equivalence and the Springer correspondence. This generalizes the result for the K = C case proved by the first two authors, and also provides a better explanation than in the earlier paper, since the current proof is uniform across all types.
Publication Source (Journal or Book title)
Representation Theory
First Page
94
Last Page
166
Recommended Citation
Achar, P., Henderson, A., & Riche, S. (2015). Geometric Satake, Springer correspondence, and small representations II. Representation Theory, 19 (6), 94-166. https://doi.org/10.1090/ert/465