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arXiv · 2312.04798

On certain varieties attached to braid representatives of a Weyl group element

Chengze Duan
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Abstract

Let $G$ be a connected reductive group over an algebraically closed field with Weyl group $W$. The analogy between Lusztig varieties and Deligne-Lusztig varieties associated to minimal length elements in elliptic conjugacy classes of $W$ was studied by He and Lusztig. In this paper, we study the parabolic version of above varieties associated to some good braid elements for any conjugacy class of $W$. This also leads to an alternative version of Lusztig's map in general case.

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Chengze Duan. 2023-12-08. On certain varieties attached to braid representatives of a Weyl group element. https://arxiv.org/abs/2312.04798

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