Hostname: page-component-54dcc4c588-trf7k Total loading time: 0 Render date: 2025-09-19T00:47:17.719Z Has data issue: false hasContentIssue false
  • English
  • Français

EXTENSION BETWEEN SIMPLE MODULES OF PRO-p-IWAHORI HECKE ALGEBRAS

Part of: Linear algebraic groups and related topics Representation theory of groups

Published online by Cambridge University Press:  20 May 2022

Noriyuki Abe Open the ORCID record for Noriyuki Abe [Opens in a new window]
Noriyuki Abe*
Affiliation:
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan
*
abenori@math.sci.hokudai.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

We calculate the extension groups between simple modules of pro-p-Iwahori Hecke algebras.

MSC classification

Primary: 20C08: Hecke algebras and their representations
Secondary: 20G25: Linear algebraic groups over local fields and their integers

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 6 , November 2023 , pp. 2775 - 2804
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abe, N., ‘A comparison between pro- $p$ Iwahori–Hecke modules and $\operatorname{mod}\ p$ representations’, Algebra Number Theory 13(8) (2019), 1959–1981.CrossRefGoogle Scholar
Abe, N., ‘Involutions on pro- $p$ -Iwahori Hecke algebras’, Represent. Theory 23 (2019), 57–87.CrossRefGoogle Scholar
Abe, N., ‘Modulo $p$ parabolic induction of pro- $p$ -Iwahori Hecke algebra’, J. Reine Angew. Math. 749 (2019), 1–64.CrossRefGoogle Scholar
Abe, N., ‘Parabolic inductions for pro- $p$ -Iwahori Hecke algebras’, Adv. Math. 355 (2019), 106776, 63.CrossRefGoogle Scholar
Abe, N., Henniart, G., Herzig, F. and Vignéras, M.-F., ‘A classification of irreducible admissible mod $p$ representations of $p$ -adic reductive groups’, J. Amer. Math. Soc. 30(2) (2017), 495–559.CrossRefGoogle Scholar
Abe, N., Henniart, G. and Vignéras, M.-F., ‘On pro- $p$ -Iwahori invariants of $R$ -representations of reductive $p$ -adic groups’, Represent. Theory 22 (2018), 119–159.CrossRefGoogle Scholar
Breuil, C. and Paškūnas, V., ‘Towards a modulo $p$ Langlands correspondence for $\mathrm{GL}_2$ ’, Mem. Amer. Math. Soc. 216(1016) (2012), vi+114.Google Scholar
Fayers, M., ‘0-Hecke algebras of finite Coxeter groups’, J. Pure Appl. Algebra 199(1–3) (2005), 27–41.CrossRefGoogle Scholar
Grosse-Klönne, E., ‘From pro- $p$ Iwahori–Hecke modules to $\left(\varphi, \varGamma \right)$ -modules, I’, Duke Math. J. 165(8) (2016), 1529–1595.CrossRefGoogle Scholar
Hauseux, J., ‘Extensions entre séries principales $p$ -adiques et modulo $p$ de $G(F)$ ’, J. Inst. Math. Jussieu 15(2) (2016), 225–270.10.1017/S1474748014000243CrossRefGoogle Scholar
Hauseux, J., ‘Compléments sur les extensions entre séries principales $p$ -adiques et modulo $p$ de $G(F)$ ’, Bull. Soc. Math. France 145(1) (2017), 161–192.CrossRefGoogle Scholar
Karol, K., ‘Homological dimension of simple pro- $p$ -Iwahori–Hecke modules’, Math. Res. Lett. 26(3) (2019), 769–804.Google Scholar
Nadimpalli, S., ‘On extensions of characters of affine pro- $p$ Iwahori–Hecke algebra’, Preprint, arXiv:1703.03110.Google Scholar
Ollivier, R., ‘Compatibility between Satake and Bernstein isomorphisms in characteristic $p$ ’, Algebra Number Theory 8(5) (2014), 1071–1111.CrossRefGoogle Scholar
Ollivier, R. and Schneider, P., ‘Pro- $p$ Iwahori–Hecke algebras are Gorenstein’, J. Inst. Math. Jussieu 13 4) (2014), 753–809.CrossRefGoogle Scholar
Paškūnas, V., ‘Extensions for supersingular representations of $\mathrm{GL}_2\left({\mathbb{Q}}_p\right)$ ’, Astérisque (331) (2010), 317–353.Google Scholar
Vignéras, M.-F., ‘Pro- $p$ -Iwahori Hecke ring and supersingular ${\overline{\mathbf{F}}}_p$ -representations’, Math. Ann. 331(3) (2005), 523–556.CrossRefGoogle Scholar
Vignéras, M.-F., ‘The pro- $p$ -Iwahori Hecke algebra of a $p$ -adic group III’, J. Inst. Math. Jussieu (2015), 1–38.Google Scholar
Vignéras, M.-F., ‘The pro- $p$ Iwahori Hecke algebra of a reductive $p$ -adic group, V (parabolic induction)’, Pacific J. Math. 279(1–2) (2015), 499–529.CrossRefGoogle Scholar
Vignéras, M.-F., ‘The pro- $p$ -Iwahori Hecke algebra of a reductive $p$ -adic group I’, Compos. Math. 152(4) (2016), 693–753.CrossRefGoogle Scholar