Abstract
Fundamental elements are certain special elements of affine Weyl groups introduced by Görtz, 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 of PEL Shimura datum, each Newton stratum contains a minimal Ekedahl–Oort stratum. This generalizes a result of Viehmann and Wedhorn.
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Notes
We can also consider the reductive group defined over the ring of Witt vectors over \(\mathbb F\). Since we use group-theoretic methods, all the results of the paper remain true.
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Acknowledgments
We would like to thank Xuhua He and Chao Zhang for helpful advice and discussions. We also thank the anonymous referee for the careful reading of the manuscript and many helpful suggestions.
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Nie, S. Fundamental elements of an affine Weyl group. Math. Ann. 362, 485–499 (2015). https://doi.org/10.1007/s00208-014-1122-7
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DOI: https://doi.org/10.1007/s00208-014-1122-7