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Geometric Structure of Affine Deligne-Lusztig Varieties for $GL_3$ (2102.09169v1)
Published 18 Feb 2021 in math.AG
Abstract: In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_3$ and $b$ basic. We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.
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