Hecke algebras and $p$-adic groups

Abstract

This survey article, is written as an extended note and supplement of my lectures in the current developments in mathematics conference in 2015. We discuss some recent developments on the conjugacy classes of affine Weyl groups and $p$-adic groups, and some applications to Shimura varieties and to representations of affine Hecke algebras.

Some corrections are made. References updated

References in corpus (10)

• 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
• Basic loci in Shimura varieties of Coxeter type
• Homological properties of representations of p-adic groups related to geometry of the group at infinity
• Affine Grassmannians and the geometric Satake in mixed characteristic
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties
• Cocenters and representations of affine $0$-Hecke algebras
• Vertexwise criteria for admissibility of alcoves
• Stratifications in the reduction of Shimura varieties

Cited by in corpus (2)

• Stratifications of affine Deligne-Lusztig varieties
• Cocenters and representations of pro-$p$ Hecke algebras