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arXiv · 2303.13289

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

Noriyuki Abe·Florian Herzig
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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.

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Noriyuki Abe, Florian Herzig. 2023-03-23. On the irreducibility of $p$-adic Banach principal series of $p$-adic $\mathrm{GL}_3$. https://doi.org/10.1007/s10013-023-00675-7

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