An irreducibility result in non-zero characteristic
The purpose of this paper is to prove that if \(F\) is a non-archimedean local field and \(G\) is an inner twist of \(GL_n/F,\) then a representation of \(G(F)\) parabolically induced from a square-integrable representation is irreducible. In the case of zero characteristic this was proved by \textit{J. N. Bernstein, P. Deligne, D. A. Kazhdan} and \textit{M.-F. Vignéras} [Représentations des groupes réductifs sur un corps local (1984; Zbl 0583.22009), Theorem B.2.d]. The present paper gives a new proof in the characteristic zero case and a proof in the case of positive characteristic. Novel aspects of the proofs are the reduction of the question of irreducibility to one about orbital integrals using the Paley-Wiener theorem of \textit{J. Bernstein, P. Deligne} and \textit{D. A. Kazhdan} [J. Anal. Math. 47, 180--192 (1986; Zbl 0634.22011)] and Kazhdan's (and Krasner's) theory of close local fields described in an article of P. Deligne in the book referred to above.
scientific article; zbMATH DE number 2157246