Cocenters of $p$-adic groups, I: Newton decomposition

Xuhua He

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arXiv · 1610.04791

Cocenters of $p$-adic groups, I: Newton decomposition

Xuhua He

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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.

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Xuhua He. 2016-10-15. Cocenters of $p$-adic groups, I: Newton decomposition. https://arxiv.org/abs/1610.04791

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