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.
Keywords
Cite
@article{arxiv.1310.2229,
title = {Fundamental elements of an affine Weyl group},
author = {Sian Nie},
journal= {arXiv preprint arXiv:1310.2229},
year = {2014}
}
Comments
Some applications to good reductions of PEL shimura varieties are added