COCENTERS OF $p$-ADIC GROUPS, I: NEWTON DECOMPOSITION. (28th March 2018)

• Record Type: Journal Article
• Authors: HE, XUHUA
• Is Part Of: Forum of mathematics. Volume 6(2018)
• Publication Date: 2018-03-28
• Subjects: 22E50 (primary), -- 20C08 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1017/fmp.2018.1
• Languages: English
• ISSNs: 2050-5086

Abstract

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.