Minuscule alcoves for \(\text{GL}_n\) and \(\text{GSP}_{2n}\)
type: Item
instance of: scholarly article
title: Minuscule alcoves for \(\text{GL}_n\) and \(\text{GSP}_{2n}\)
zbMATH Open document ID: 0981.17003
author: Michael Rapoport
author: Robert Kottwitz
published in: Manuscripta Mathematica
publication date: 2001-08-19T00:00:00Z
review text: The aim of this paper is to study the extended affine Weyl group \(\widetilde{W}\) for \(\text{GL}_n\). Let \(\mu\) be a minuscule coweight for either \(\text{GL}_N\) or \(\text{GSp}_{2n}\) and regard \(\mu\) as an element \(t_\mu\) in the extended affine Weyl group \(\widetilde{W}\). Say an element \(x\in\widetilde{W}\) is \(\mu\)-admissible if there exists \(\mu'\) in the Weyl group orbit of \(\mu\) such that \(x\leq t_{\mu'}\) in the Bruhat order on \(\widetilde{W}\). The main result Theorem 3.5(3) is that \(x\in\widetilde{W}\) is \(\mu\)-admissible if and only if it is \(\mu\)-permissible, where \(\mu\)-permissibility is defined using inequalities arising naturally in the study of bad reduction of Shimura varieties. Moreover, the authors show Theorem 4.5(3) as a completely analogous result for the group \(G = \text{GSp}_{2n}\), of symplectic similitudes.
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1542480
zbMATH Keywords: affine Weyl group
zbMATH Keywords: minuscule coweight
zbMATH Keywords: minuscule alcoves
reviewed by: Fang Li
MaRDI profile type: Publication
full work available at URL: s002290070034
OpenAlex ID: W1989451605
DOI: 10.1007/S002290070034
description: scientific article; zbMATH DE number 1542480