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An Iwahori-Whittaker model for the Satake category

Roman Bezrukavnikov 1 Dennis Gaitsgory 2 Ivan Mirkovic 3 Simon Riche 4, 5 Laura Rider 6
1 MIT - Massachusetts Institute of Technology
2 HARVARD - Department of Mathematics [Cambridge]
3 UMass Amherst - University of Massachusetts [Amherst]
4 LMBP - Laboratoire de Mathématiques Blaise Pascal - Clermont Auvergne
5 UCA - Université Clermont Auvergne
6 University of Georgia [USA]
Abstract : In this paper we prove, for G a connected reductive algebraic group satisfying a technical assumption, that the Satake category of G (with coefficients in a finite field, a finite extension of Q_l, or the ring of integers of such a field) can be described via Iwahori-Whittaker perverse sheaves on the affine Grassmannian. As an application, we confirm a conjecture of Juteau-Mautner-Williamson describing the tilting objects in the Satake category.
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  • HAL Id : hal-01818403, version 1

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CNRS | INSMI | PRES_CLERMONT | UMR6620 | ACL-SF

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Roman Bezrukavnikov, Dennis Gaitsgory, Ivan Mirkovic, Simon Riche, Laura Rider. An Iwahori-Whittaker model for the Satake category. Journal de l'École polytechnique — Mathématiques, École polytechnique, 2019, 6, pp.707-735. ⟨hal-01818403⟩

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