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

2023/12/08 by Duan, Chengze
#20C33 #20G05 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2312.04798

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.

Related

• Geometry and cohomology of compactified Deligne--Lusztig varieties
• Lusztig varieties for regular elements
• Connected components of closed affine Deligne-Lusztig varieties
• Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes
• Good position braid representatives and transversal slices of unipotent orbits