Involutions on pro-$p$-Iwahori Hecke algebras
Author:
Noriyuki Abe
Journal:
Represent. Theory 23 (2019), 57-87
MSC (2010):
Primary 20C08, 20G25
DOI:
https://doi.org/10.1090/ert/521
Published electronically:
January 22, 2019
MathSciNet review:
3902325
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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.
Article copyright:
© Copyright 2019
American Mathematical Society
