Dimensions of Affine Deligne-Lusztig Varieties: A New Approach Via Labeled Folded Alcove Walks and Root Operators

by Elizabeth Miliaceviac, Petra Schwer, Elizabeth Milicevic, et al.

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 Rapoport. Basic questions about the varieties $X_x(b)$ which have remained largely open include when they are nonempty, and if nonempty, their dimension...

• Format: Paperback
• Language: English
• ISBN: 1470436760
• ISBN13: 9781470436766
• Release Date: December 2019
• Publisher: American Mathematical Society
• Length: 101 Pages