COCENTERS OF -ADIC GROUPS, I: NEWTON DECOMPOSITION
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.
2011 ◽
Vol 63
(5)
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pp. 1137-1160
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2020 ◽
Vol 30
(07)
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pp. 1505-1535
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1998 ◽
Vol 46
(11-12)
◽
pp. 1525-1534
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