On the Hodge-Newton decomposition for split groups

2003/07/03 by Robert E. Kottwitz
Mathematics · #math.RT #msc:11S25 #msc:14L05 #msc:14F30

paper · pdf

published as Internat. Math. Res. Notices 26 (2003), 1433-1447

arxiv created 2003/07/03 · arxiv updated 2009/11/30

Abstract

The main purpose of this paper is to prove a group-theoretic generalization of a theorem of Katz on isocrystals. Along the way we reprove the group-theoretic generalization of Mazur's inequality for isocrystals due to Rapoport-Richartz, and generalize from split groups to unramified groups a result of Kottwitz-Rapoport which determines when an affine Deligne-Lusztig subset of the affine Grassmannian is non-empty.

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