Good position braid representatives and transversal slices of unipotent orbits

2023/10/19 by Chengze Duan, Duan, Chengze
Mathematics · #20E45 #20F55 #20G99 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2310.12750

openalex publication_date 2023/10/19 · openalex created_date 2023/10/21 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive group over an algebraically closed field and W be its Weyl group. Steinberg constructed a transversal slice of the regular unipotent orbit in G. This construction was generalized to n was generalized to unipotent orbits associated to any elliptic conjugacy classes of W by He and Lusztig via good minimal length elements. In this paper, we construct transversal slices for all unipotent orbits using the good elements in the associated braid monoid of W. As an application, we reformulate the dimension formula of affine Springer fibers using these good elements.

Related

• From braids to transverse slices in reductive groups
• On certain varieties attached to braid representatives of a Weyl group element
• Inequalities characterizing distinguished unipotent orbits
• The sections of the Weyl group
• Remarks on Springer's representations