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Representation Theory

ISSN 1088-4165



Involutions on pro-$p$-Iwahori Hecke algebras

Author: Noriyuki Abe
Journal: Represent. Theory 23 (2019), 57-87
MSC (2010): Primary 20C08, 20G25
Published electronically: January 22, 2019
MathSciNet review: 3902325
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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.

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Additional Information

Noriyuki Abe
Affiliation: Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan
MR Author ID: 858099

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.
Article copyright: © Copyright 2019 American Mathematical Society