On irreducible supersingular representations of ${\mathrm{GL}}_2(F)$

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.

11 pages

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