Notes on partial conjugation

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.

11 pages. To appear in ICCM 2010 proceeding

References in corpus (4)

• A guide to the reduction modulo p of Shimura varieties
• Introduction to Shimura varieties with bad reduction of parahoric type
• Minimal length elements in conjugacy classes of extended affine Weyl group
• Parabolic character sheaves, III