关于SO(4)的细化局部逆定理
On a refined local converse theorem for SO(4)
AI总结：
本文针对SO(4)的局部逆定理问题，通过引入额外的扭曲伽马因子，证明了广义超 cuspidal 表示的唯一性。
摘要：
最近，Hazeltine-Liu和独立地Haan-Kim-Kwon为p-adic域F上的SO_{2n}(F)证明了一个局部逆定理，该定理表明，除了SO_{2n}(F)的外自同构外，不可约广义表示由GL_k(F)上的广义伽马因子唯一确定，其中k=1,…,n。希望用更多的扭曲伽马因子去除上述定理中的“除外自同构”部分，但这个问题似乎很困难。在本文中，我们为群SO_4(F)提供了该问题的解决方案，即证明广义超 cuspidal 表示π of SO_4(F)由其GL_1、GL_2扭曲局部伽马因子和π的扭曲外平方局部伽马因子唯一确定。
英文摘要：
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 $π$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
