Cocenters of p-adic groups, I: Newton decomposition

2016/10/15 by Xuhua He, He, Xuhua
Mathematics · #20C08 #22E50 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C08 #msc:22E50

paper · pdf · doi:10.48550/arxiv.1610.04791

20 pages. Final version to appear in Forum of Mathematics, Pi

arxiv created 2018/03/08 · arxiv updated 2018/03/09

Abstract

In this paper, we introduce the Newton decomposition on a connected reductive p-adic group G. Based on it we give a nice decomposition of the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the usual conjugation action on G and the twisted cocenter arising from the theory of twisted endoscopy. We give Iwahori-Matsumoto type generators on the Newton components of the cocenter. Based on it, we prove a generalization of Howe's conjecture on the restriction of (both ordinary and twisted) invariant distributions. Finally we give an explicit description of the structure of the rigid cocenter.

Related

• Cocenter of p-adic groups, II: induction map
• Jordan Decompositions of cocenters of reductive p-adic groups
• Cocenters of p-adic groups, III: Elliptic and rigid cocenters
• A geometric interpretation of Newton strata
• Geometric structure in the principal series of the p-adic group G₂