## Involutions on pro-$p$-Iwahori Hecke algebras

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- by Noriyuki Abe
- Represent. Theory
**23**(2019), 57-87 - DOI: https://doi.org/10.1090/ert/521
- Published electronically: January 22, 2019
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## Abstract:

The pro-$p$-Iwahori Hecke algebra has an involution $\iota$ defined in terms of the Iwahori-Matsumoto basis. Then for a module $\pi$ of pro-$p$-Iwahori Hecke, $\pi ^\iota = \pi \circ \iota$ is also a module. We calculate $\pi ^\iota$ for simple modules $\pi$. We also calculate the dual of $\pi$. These calculations will be used for calculating the extensions between simple modules.## References

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## Bibliographic Information

**Noriyuki Abe**- Affiliation: Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan
- MR Author ID: 858099
- Email: abenori@math.sci.hokudai.ac.jp
- Received by editor(s): February 6, 2018
- Received by editor(s) in revised form: September 30, 2018
- Published electronically: January 22, 2019
- Additional Notes: The work was supported by JSPS KAKENHI Grant Number 26707001.
- © Copyright 2019 American Mathematical Society
- Journal: Represent. Theory
**23**(2019), 57-87 - MSC (2010): Primary 20C08, 20G25
- DOI: https://doi.org/10.1090/ert/521
- MathSciNet review: 3902325