Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.06256 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Recently, Hazeltine-Liu, and independently Haan-Kim-Kwon, proved a local converse theorem for $\mathrm{SO}_{2n}(F)$ over a $p$-adic field $F$, which says that, up to an outer automorphism of $\mathrm{SO}_{2n}(F)$, an irreducible generic representation of $\mathrm{SO}_{2n}(F)$ is uniquely determined by its twisted gamma factors by generic representations of $\mathrm{GL}_k(F)$ for $k=1,\dots,n$. It is desirable to remove the ``up to an outer automorphism" part in the above theorem using more twisted gamma factors, but this seems a hard problem. In this paper, we provide a solution to this problem for the group $\mathrm{SO}_4(F)$, namely, we show that a generic supercuspidal representation $π$ of $\mathrm{SO}_4(F)$ is uniquely determined by its $\mathrm{GL}_1$, $\mathrm{GL}_2$ twisted local gamma factors and a twisted exterior square local gamma factor of $π$.