Vol. 315, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 317: 1
Vol. 316: 1  2
Vol. 315: 1  2
Vol. 314: 1  2
Vol. 313: 1  2
Vol. 312: 1  2
Vol. 311: 1  2
Vol. 310: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Iwahori–Hecke model for mod $p$ representations of $\mathrm{GL}(2,F)$

U. K. Anandavardhanan and Arindam Jana

Vol. 315 (2021), No. 2, 255–283
DOI: 10.2140/pjm.2021.315.255
Abstract

For a p-adic field F, the space of pro-p-Iwahori invariants of a universal supersingular mod p representation τ of GL2(F) is determined in the works of Breuil, Schein, and Hendel. The representation τ is introduced by Barthel and Livné and is defined in terms of the spherical Hecke operator. In Anandavardhanan and Borisagar [2013; 2015], an Iwahori–Hecke approach was introduced to study these universal supersingular representations in which they can be characterized via the Iwahori–Hecke operators. In this paper, we construct a certain quotient π of τ, making use of the Iwahori–Hecke operators. When F is not totally ramified over p, the representation π is a nontrivial quotient of τ. We determine a basis for the space of invariants of π under the pro-p-Iwahori subgroup. A pleasant feature of this “new” representation π is that its space of pro-p-Iwahori invariants admits a more uniform description vis-à-vis the description of the space of pro-p-Iwahori invariants of τ.

Keywords
modular representations, supersingular representations, Iwahori–Hecke model
Mathematical Subject Classification
Primary: 20G05
Secondary: 11F70, 22E50
Milestones
Received: 21 February 2021
Revised: 7 September 2021
Accepted: 1 November 2021
Published: 19 January 2022
Authors
U. K. Anandavardhanan
Department of Mathematics
Indian Institute of Technology Bombay
Mumbai
India
Arindam Jana
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India
Department of Mathematics
Indian Institute of Technology Bombay
Mumbai
India