Non-admissible modulo $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_{p^2})$

Abstract: The notion of admissibility of representations of $p$-adic groups goes back to Harish-Chandra. Jacquet, Bernstein and Vigneras have shown that smooth irreducible representations of connected reductive $p$-adic groups over algebraically closed fields of characteristic different from $p$ are admissible.

We use a Diamond diagram attached to a $2$-dimensional reducible split mod $p$ Galois representation of $\mathrm{Gal}_{\mathbb{Q}_{p^2}}$ to construct a non-admissible smooth irreducible mod $p$ representation of $\mathrm{GL}_2(\mathbb{Q}_{p^2})$ following the approach of Daniel Le.

This is joint work with Mihir Sheth.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar