GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES

By Xuhua He. 2012

94 citations recorded by the source corpus.

This paper studies ane Deligne-Lusztig varieties X ~ w(b) in the ane ag variety of a quasi-split tamely ramied group. We describe the geometric structure of X ~ w(b) for a minimal length element ~ w in the conjugacy class of an extended ane Weyl group. We then provide a reduction method that relates the structure of X ~ w(b) for arbitrary elements ~ w in the extended ane Weyl group to those associated with minimal length elements. Based on this reduction, we establish a connection between the dimension of ane Deligne-Lusztig varieties and the degree of the class polynomial of ane ~

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e99bdf0a45e4581500f2ece2b4d0c7e222439a4

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. S. Nie
2. Xuhua He
3. Michael Rapoport

In Geometry and Topology

1. S. Nie
2. Xuhua He
3. Michael Rapoport

In Mathematical Physics

1. S. Nie
2. Xuhua He

Citations in the corpus

• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties (2014, methodology): “The proof is based on the reductive method in [10] à la Deligne and Lusztig, some remarkable combinatorial properties on W̃ established in [11] and the Grothendieck conjecture for split groups proved by Viehmann in [24].”
• Minimal length elements of extended affine Weyl groups (2011, background): “Moreover, Theorem B is a crucial ingredient in the study of affine Deligne–Lusztig varieties in [He14].”