On the Hodge-Newton decomposition for split groups

Details On the Hodge-Newton decomposition for split groups On the Hodge-Newton decomposition for split groups

2003-07-03

arxiv.org/abs/math/0307052v1

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

Mathematics

Representation Theory

Scientific paper

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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