manuscripta mathematica

, Volume 102, Issue 4, pp 403–428

Minuscule alcoves for GLn and GSp2n

  • R. Kottwitz
  • M. Rapoport

DOI: 10.1007/s002290070034

Cite this article as:
Kottwitz, R. & Rapoport, M. manuscripta math. (2000) 102: 403. doi:10.1007/s002290070034


Let μ be a minuscule coweight for either GLn or GSp2n, and regard μ as an element tμ in the extended affine Weyl group \(\). We say that an element \(\) is μ-admissible if there exists μ′ in the Weyl group orbit of μ such that xtμ′ in the Bruhat order on \(\). Our main result is that \(\) is μ-admissible if and only if it is μ-permissible, where μ-permissibility is defined using inequalities arising naturally in the study of bad reduction of Shimura varieties.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • R. Kottwitz
    • 1
  • M. Rapoport
    • 2
  1. 1.Mathematics Department, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA. e-mail: kottwitz@math.uchicago.eduUS
  2. 2.Mathematisches Institut der Universität zu Köln, Weyertal 86–90, 50931 Köln, GermanyDE