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arXiv · 2102.09169

Geometric Structure of Affine Deligne-Lusztig Varieties for $GL_3$

Ryosuke Shimada
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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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Ryosuke Shimada. 2021-02-18. Geometric Structure of Affine Deligne-Lusztig Varieties for $GL_3$. https://arxiv.org/abs/2102.09169

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