Test vectors for trilinear forms : the case of two principal series

Abstract

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero linear form exists, one wants to find an element of V which is not in its kernel: this is a test vector. Gross and Prasad found explicit test vectors when the three representations are unramified principal series, and when they are all unramified twists of the Steinberg representation. In this paper we decribe explicit test vectors when two of the representations are principal series.