Affine Deligne–Lusztig varieties in affine flag varieties
By Ulrich Goertz, Thomas J. Haines, R. Kottwitz, Daniel C. Reuman. Compositio Mathematica, 2008
88 citations recorded by the source corpus.
Abstract This paper studies affine Deligne–Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, and extends previous conjectures concerning their dimensions. We generalize the superset method, an algorithmic approach to the questions of non-emptiness and dimension. Our non-emptiness results apply equally well to the p-adic context and therefore relate to moduli of p-divisible groups and Shimura varieties with Iwahori level structure.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f23328d4182b051fa52c9a278d548f4c33a940a1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES (2012, result): “It is proved in [10], [8] for a split group and [11, Theorem B] for any tamely ramified group that if w̃ ∈ W̃ ′ and b ∈ G(L) is a basic element with κ(w̃) = κ(b), then Xw̃(b) 6= ∅ if and only if suppδ(ηδ(w̃)) = S.”
- Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties (2014, background): “If K is an Iwahori subgroup and b is basic, a conjecture on the non-emptiness pattern (for split groups) is given by Görtz, Haines, Kottwitz, and Reuman in [3] in terms of P -alcoves in [3] and the generalization of this conjecture to any tamely ramified groups is proved”