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An Iwahori-Whittaker model for the Satake category

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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Submitted on : Tuesday, June 19, 2018 - 9:42:36 AM
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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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