On irreducible supersingular representations of $\mathrm{GL}_{2}(F)$

Mihir Sheth

Vol. 321 (2022), No. 2, 431–442

DOI: 10.2140/pjm.2022.321.431

Abstract

Let $F$ be a nonarchimedean local field of residual characteristic $p>3$ and residue degree $f>1$. We study a certain type of diagram, called cyclic  diagrams, and use them to show that the universal supersingular modules of ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_2(F)$ admit infinitely many nonisomorphic irreducible admissible quotients.

Keywords

supersingular representations, diagrams

Mathematical Subject Classification

Primary: 22E50

Secondary: 11S37

Milestones

Received: 1 December 2021

Revised: 28 September 2022

Accepted: 14 November 2022

Published: 21 March 2023