Journal of the Ramanujan Mathematical Society

Volume 31, Issue 2, June 2016 pp. 109–124.

Base change and (GL n (F), GL n-1 (F))-distinction

Authors: Arnab Mitra and C. G. Venketasubramanian
Author institution:Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

Summary: Let F be a nonarchimedean local field and E a finite cyclic extension of F of prime degree d. Further let G n-1 be embedded into G n as block matrices in the usual way. It is not true in general that the base change lift of a G n-1 (F)-distinguished representation of G n(F) is G n-1 (E)-distinguished. We obtain a precise condition for an irreducible G n-1 (F)-distinguished representation π of G n(F) to be taken to a G n-1 (E)-distinguished representation by the base change map. If π is unitarizable and G n-1 (F)-distinguished, then we show that the base change lift of π is G n-1 (E)-distinguished. We then analyse the fiber of the base change map over a G n-1 (E)-distinguished representation of G n(E) and determine the number of G n-1 (F)-distinguished representations in the fiber.

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