Geodesic
COCENTERS OF $p$ -ADIC GROUPS, I: NEWTON DECOMPOSITION
Forum of Mathematics, Pi, Tome 6 (2018)

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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. 
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     author = {XUHUA HE},
     title = {COCENTERS {OF} $p$ {-ADIC} {GROUPS,} {I:} {NEWTON} {DECOMPOSITION}},
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XUHUA HE. COCENTERS OF $p$ -ADIC GROUPS, I: NEWTON DECOMPOSITION. Forum of Mathematics, Pi, Tome 6 (2018). doi: 10.1017/fmp.2018.1

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