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Journal Articles Journal de l'École polytechnique — Mathématiques Year : 2019

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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Dates and versions

hal-01818403 , version 1 (19-06-2018)

Identifiers

  • HAL Id : hal-01818403 , version 1

Cite

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