## Cocenters and representations of pro-$p$ Hecke algebras

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- by Xuhua He and Sian Nie
- Represent. Theory
**21**(2017), 82-105 - DOI: https://doi.org/10.1090/ert/498
- Published electronically: June 23, 2017
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## 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 $\overline {\tilde {\mathcal H}}$.## References

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## Bibliographic Information

**Xuhua He**- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 733194
- Email: xuhuahe@math.umd.edu
**Sian Nie**- Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China
- Email: niesian@amss.ac.cn
- Received by editor(s): May 11, 2016
- Received by editor(s) in revised form: October 10, 2016, December 1, 2016, February 26, 2017, and May 10, 2017
- Published electronically: June 23, 2017
- Additional Notes: The first author was partially supported by NSF DMS-1463852. The second author was partially supported by NSFC (No. 11501547 and No. 11621061.) and by the Key Research Program of Frontier Sciences, CAS, Grant No. QYZDB-SSW-SYS007.
- © Copyright 2017 American Mathematical Society
- Journal: Represent. Theory
**21**(2017), 82-105 - MSC (2010): Primary 20C08, 20C20, 22E50
- DOI: https://doi.org/10.1090/ert/498
- MathSciNet review: 3665615