# MathSciDoc: An Archive for Mathematician ∫

#### Representation Theorymathscidoc:1912.43233

Representation Theory of the American Mathematical Society, 21, (6), 82-105, 2017
In this paper, we study the relation between the cocenter \overline {{ilde {\mathcal H}}} and the representations of an affine pro-\overline {{ilde {\mathcal H}}} Hecke algebra \overline {{ilde {\mathcal H}}} . As a consequence, we obtain a new criterion on supersingular representations: a (virtual) representation of \overline {{ilde {\mathcal H}}} is supersingular if and only if its character vanishes on the non-supersingular part of the cocenter \overline {{ilde {\mathcal H}}} .
@inproceedings{xuhua2017cocenters,
title={Cocenters and representations of pro- Hecke algebras},
author={Xuhua He, and Sian Nie},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113102097706793},
booktitle={Representation Theory of the American Mathematical Society},
volume={21},
number={6},
pages={82-105},
year={2017},
}

Xuhua He, and Sian Nie. Cocenters and representations of pro- Hecke algebras. 2017. Vol. 21. In Representation Theory of the American Mathematical Society. pp.82-105. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113102097706793.