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