Notes on partial conjugation

2011/10/08 by Chuying Fang, Fang, Chuying, Xuhua He +1
Mathematics · #20E45 #20F55 #20G25 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1110.1689

openalex publication_date 2011/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this notes, we will give an exposition of some results on the method of partial conjugation action. We first discuss the partial conjugation action of a parabolic subgroup of a Coxeter group. We then discuss some applications to Lusztig's G-stable pieces and its affine generalization. We also discuss some recent work on the \s-conjugacy classes of loop groups and affine Deligne-Lusztig varieties.

Citations

• Introduction to Shimura varieties with bad reduction of parahoric type
• A guide to the reduction modulo p of Shimura varieties

Related

• Parabolic Conjugation and Commuting Varieties
• Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes
• Conjugacy classes of involutions and Kazhdan-Lusztig cells
• Minimally dominant elements of finite Coxeter groups
• Conjugation on varieties of nilpotent matrices