Cocenters and representations of pro-𝑝 Hecke algebras

He, Xuhua; Nie, Sian

doi:10.1090/ert/498

Cocenters and representations of pro-$p$ Hecke algebras
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Represent. Theory 21 (2017), 82-105 Request permission

Abstract:

In this paper, we study the relation between the cocenter $\overline {{\tilde {\mathcal H}}}$ and the representations of an affine pro-$p$ Hecke algebra ${\tilde {\mathcal H}}={\tilde {\mathcal H}}(0, -)$. As a consequence, we obtain a new criterion on supersingular representations: a (virtual) representation of ${\tilde {\mathcal H}}$ is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter $\overline {\tilde {\mathcal H}}$.

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