Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes

2020/04/03 by Jeffrey Adams, Adams, Jeffrey, Xuhua He +3
Mathematics · #20E45 #20F55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Primary: 20G07 #Representation Theory (math.RT) #Secondary: 06A07

paper · pdf · doi:10.48550/arxiv.2004.01337

openalex publication_date 2020/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a reductive group over an algebraically closed field and let W be its Weyl group. In a series of papers, Lusztig introduced a map from the set [W] of conjugacy classes of W to the set [G_u] of unipotent classes of G. This map, when restricted to the set of elliptic conjugacy classes [W_e] of W, is injective. In this paper, we show that Lusztig's map [W_e] → [G_u] is order-reversing, with respect to the natural partial order on [W_e] arising from combinatorics and the natural partial order on [G_u] arising from geometry.

Related

• From conjugacy classes in the Weyl group to unipotent classes, II
• From conjugacy classes in the Weyl group to unipotent classes
• From unipotent classes to conjugacy classes in the Weyl group
• From conjugacy classes in the Weyl group to unipotent classes, III
• Distinguished conjugacy classes and elliptic Weyl group elements