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Hecke algebras and $p$-adic groups

Hecke algebras and $p$-adic groups

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 …