A PROOF OF THE FINITE FIELD ANALOGUE OF JACQUET'S CONJECTURE

In this paper, the proof of the finite-field-analogue of Jacquet's conjecture on local converse theorem for cuspidal representations of general linear groups is given. More precisely, the set of twisted gamma factors of π, $\left\{\mathrm{\gamma }\right(\mathrm{\pi }\times \mathrm{\tau },\mathrm{\psi }\left)\right|\mathrm{\tau }\in {\mathrm{G}}_{\mathrm{t}},1\le \mathrm{t}\le \left[\frac{\mathrm{n}}{2}\right]\}$, together with a central character ωπ, determine uniquely (up to isomorphism) the irreducible cuspidal representation π of GLn(Fq), where Gt denotes the set of irreducible generic representations of GLt(Fq), and Fq denotes a finite field of q elements.