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Authors
Affiliations
1 Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, IL
Source
Journal of the Ramanujan Mathematical Society, Vol 31, No 2 (2016), Pagination: 109-124
Abstract
Let F be a nonarchimedean local field and E a finite cyclic extension of F of prime degree d. Further let GLn-1 be embedded into GLn as block matrices in the usual way. It is not true in general that the base change lift of a GLn-1(F)-distinguished representation of GLn(F) is GLn-1(E)-distinguished. We obtain a precise condition for an irreducible GLn-1(F)-distinguished representation π of GLn(F) to be taken to a GLn-1(E)-distinguished representation by the base change map. If π is unitarizable and GLn-1(F)-distinguished, then we show that the base change lift of π is GLn-1(E)-distinguished. We then analyse the fiber of the base change map over a GLn-1(E)-distinguished representation of GLn(E) and determine the number of GLn-1(F)-distinguished representations in the fiber.
