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.
- N. Abe, Modulo $p$ parabolic induction of pro-$p$-Iwahori Hecke algebra, J. Reine Angew. Math., DOI:10.1515/crelle-2016-0043.
- N. Abe, Parabolic inductions for pro-$p$-Iwahori Hecke algebras, arXiv:1612.01312.
- N. Abe, Extension between simple modules of pro-$p$-Iwahori Hecke algebras, arXiv:1705.00728.
- N. Abe, G. Henniart, F. Herzig, and M.-F. Vignéras, A classification of irreducible admissible ${\rm mod}\, p$ representations of $p$-adic reductive groups, J. Amer. Math. Soc. 30 (2017), no. 2, 495–559. MR 3600042, DOI https://doi.org/10.1090/jams/862
- Marie-France Vignéras, The pro-$p$ Iwahori Hecke algebra of a reductive $p$-adic group, V (parabolic induction), Pacific J. Math. 279 (2015), no. 1-2, 499–529. MR 3437789, DOI https://doi.org/10.2140/pjm.2015.279.499
- Vinay V. Deodhar, Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math. 39 (1977), no. 2, 187–198. MR 435249, DOI https://doi.org/10.1007/BF01390109
- Rachel Ollivier, Compatibility between Satake and Bernstein isomorphisms in characteristic $p$, Algebra Number Theory 8 (2014), no. 5, 1071–1111. MR 3263136, DOI https://doi.org/10.2140/ant.2014.8.1071
- Marie-France Vignéras, The pro-$p$ Iwahori Hecke algebra of a reductive $p$-adic group, V (parabolic induction), Pacific J. Math. 279 (2015), no. 1-2, 499–529. MR 3437789, DOI https://doi.org/10.2140/pjm.2015.279.499
- Marie-France Vigneras, The pro-$p$-Iwahori Hecke algebra of a reductive $p$-adic group I, Compos. Math. 152 (2016), no. 4, 693–753. MR 3484112, DOI https://doi.org/10.1112/S0010437X15007666
- Marie-France Vigneras, The pro-$p$-Iwahori Hecke algebra of a reductive $p$-adic group III (spherical Hecke algebras and supersingular modules), J. Inst. Math. Jussieu 16 (2017), no. 3, 571–608. MR 3646282, DOI https://doi.org/10.1017/S1474748015000146
Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20C08, 20G25
Retrieve articles in all journals with MSC (2010): 20C08, 20G25
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