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arXiv · 2501.15827

Lusztig varieties for regular elements

Xuhua He·Ruben La
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Abstract

Let $G$ be a connected reductive group over an algebraically closed field. Let $B$ be a Borel subgroup of $G$ and $W$ be the associated Weyl group. We show that for any $w \in W$ that is not contained in any standard parabolic subgroup of $W$, the intersection of the Bruhat cell $B w B$ with any regular conjugacy class of $G$ is always irreducible. We then prove that the associated Lusztig varieties are irreducible. This extends the previous work of Kim \cite{kim2020homology} on the regular semisimple and regular unipotent elements. The irreducibilitiy result of Lusztig varieties will be used in an upcoming work in the study of affine Lusztig varieties.

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Xuhua He, Ruben La. 2025-01-27. Lusztig varieties for regular elements. https://arxiv.org/abs/2501.15827

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