Dimensions of Affine Deligne–Lusztig Varieties: A New Approach via Labeled Folded Alcove Walks and Root Operators
Let $G$ be a reductive group over the field $F=k((t))$, where $k$ is an algebraic closure of a finite field, and let $W$ be the (extended) affine Weyl group of $G$. The associated affine Deligne-Lusztig varieties $X_x(b)$, which are indexed by elements $b \in G(F)$ and $x \in W$, were introduced by...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2019
|
| Schriftenreihe: | Memoirs of the American Mathematical Society |
| ISBN: | 9781470436766, 1470436760 |
| ISSN: | 0065-9266, 1947-6221 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- Introduction -- Preliminaries on Weyl groups, affine buildings, and related notions -- Labelings and orientations, galleries, and alcove walks -- Dimensions of galleries and root operators -- Affine Deligne–Lusztig varieties and folded galleries -- Explicit constructions of positively folded galleries -- The varieties <inline-formula content-type="math/mathml"> X x ( 1 ) X_x(1) </inline-formula> in the shrunken dominant Weyl chamber -- The varieties <inline-formula content-type="math/mathml"> X x ( 1 ) X_x(1) </inline-formula> and <inline-formula content-type="math/mathml"> X x ( b ) X_x(b) </inline-formula> -- Conjugating to other Weyl chambers -- Diagram automorphisms -- Applications to affine Hecke algebras and affine reflection length