On the irreducibility of $p$-adic Banach principal series of $p$-adic ${\mathrm{GL}}_3$

Abstract

We establish an optimal (topological) irreducibility criterion for $p$-adic Banach principal series of ${\mathrm{GL}}_n(F)$, where $F/{\mathbb{Q}}_p$ is finite and $n\le 3$. This is new for $n=3$ as well as for $n=2$, $F\ne {\mathbb{Q}}_p$ and establishes a refined version of Schneider's conjecture [Sch06, Conjecture 2.5] for these groups.

21 pages. Slightly revised from the published version to update references to our companion paper

References in corpus (1)

• On the irreducibility of $p$-adic Banach principal series of $p$-adic ${\mathrm{GL}}_3$

Cited by in corpus (1)

• On the irreducibility of $p$-adic Banach principal series of $p$-adic ${\mathrm{GL}}_3$