Dimensions of affine Deligne-Lusztig varieties : a new approach via labeled folded alcove walks and root operators - Milićević, Elizabeth; Schwer, Petra; Thomas, Anne (Mathematician) (Memoirs of the American Mathematical Society, 2019)
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. The authors use techniques inspired by geometric group theory and combinatorial representation theory to address these questions in the case that b is a pure transl.