# Dimensions of Affine Deligne–Lusztig Varieties: A New Approach via Labeled Folded Alcove Walks and Root Operators

@article{Milicevic2019DimensionsOA, title={Dimensions of Affine Deligne–Lusztig Varieties: A New Approach via Labeled Folded Alcove Walks and Root Operators}, author={Elizabeth Milicevic and Petra Schwer and Anne Thomas}, journal={Memoirs of the American Mathematical Society}, year={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 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. We use techniques inspired by geometric group theory and representation…

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