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

DOI10.2140/PJM.2022.321.431arXiv2210.07283MaRDI QIDQ6413874

Mihir Sheth

Publication date: 13 October 2022

Abstract: Let $F$ be a non-archimedean local field of residual characteristic $p>3$ and residue degree $f>1$. We study a certain type of diagram, called emph{cyclic diagrams}, and use them to show that the universal supersingular modules of $mathrm{GL}_2(F)$ admit infinitely many non-isomorphic irreducible admissible quotients.

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over local fields (22E50) Langlands-Weil conjectures, nonabelian class field theory (11S37)

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