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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
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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
Email: abenori@math.sci.hokudai.ac.jp

DOI: https://doi.org/10.1090/ert/521
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