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Cocenters and representations of pro- Hecke algebras

Xuhua He Sian Nie

Representation Theory mathscidoc: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}}} .
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@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.
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