Cocenters of <i>p</i>-adic Groups, III: Elliptic and Rigid Cocenters

Dan Ciubotaru; Xuhua He

doi:10.1007/s42543-020-00027-1

Peking Mathematical Journal ›› 2020, Vol. 4 ›› Issue (2) : 159-186. DOI: 10.1007/s42543-020-00027-1

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Cocenters of p-adic Groups, III: Elliptic and Rigid Cocenters

Dan Ciubotaru¹ ,
Xuhua He²^,^b

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Abstract

In this paper, we show that the elliptic cocenter of the Hecke algebra of a connected reductive p-adic group is contained in the rigid cocenter. As applications, we prove the trace Paley–Wiener theorem and the abstract Selberg principle for mod-l representations.

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Dan Ciubotaru, Xuhua He. Cocenters of p-adic Groups, III: Elliptic and Rigid Cocenters. Peking Mathematical Journal, 2020, 4(2): 159‒186 https://doi.org/10.1007/s42543-020-00027-1