Middle supercuspidals of GL(2N,F) are characterized by twisted gamma factors against tamely ramified quasi-characters and simple supercuspidals of GL(N,F).
On the sharpness of the bound for the local converse theorem of p-adic GL_N, general N
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abstract
Let F be a non-archimedean local field of characteristic zero. In this paper we construct examples of supercuspidal representations showing that the bound $[N/2]$ for the local converse theorem of $GL_N(F)$ is sharp, N general, when the residual characteristic of $F$ is bigger than $N$.
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On the Local Converse Theorem for Depth $\frac{1}{N}$ Supercuspidal Representations of $\text{GL}(2N, F)$
Middle supercuspidals of GL(2N,F) are characterized by twisted gamma factors against tamely ramified quasi-characters and simple supercuspidals of GL(N,F).