


























Abstract:Smith-Treumann localization for sheaves on the affine Grassmannian of a reductive group has previously been studied by Leslie-Lonergan (for spherical sheaves) and by Riche-Williamson (for Iwahori-Whittaker sheaves). In this paper, we show that the two versions are related by a commutative diagram that involves "convolution with the Steinberg module."
As an application, we "categorify" certain formal characters of a reductive group called Steinberg quotients, previously introduced and studied by the second author. Specifically, we show that Steinberg quotients describe the stalks of spherical parity sheaves on the $\mathbb{Z}/p\mathbb{Z}$-fixed-locus of the affine Grassmannian.
From: Pramod N. Achar [view email]
[v1]
Fri, 19 Jun 2026 19:09:44 UTC (49 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。