Fundamental elements of an affine Weyl group

Abstract

Fundamental elements are certain special elements of affine Weyl groups introduced by Gortz, Haines, Kottwitz and Reuman. They play an important role in the study of affine Deligne-Lusztig varieties. In this paper, we obtain characterizations of the fundamental elements and their natural generalizations. We also derive an inverse to a version of "Newton-Hodge decomposition" in affine flag varieties. As an application, we obtain a group-theoretic generalization of Oort's results on minimal p-divisible groups, and we show that, in certain good reduction reduction of PEL Shimura datum, each Newton stratum contains a minimal Ekedahl-Oort stratum. This generalizes a result of Viehmann and Wedhorn.

Some applications to good reductions of PEL shimura varieties are added

References in corpus (4)

• Ekedahl-Oort and Newton strata for Shimura varieties of PEL type
• Minimal length elements of extended affine Coxeter groups, II
• $P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties
• $P$-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras

Cited by in corpus (3)

• Stratifications and foliations for good reductions of Shimura varieties of Hodge type
• Sections of the Hodge bundle over Ekedahl-Oort strata of Shimura varieties of Hodge type
• On isomorphism numbers of "$F$-crystals"