Classification of standard modules with linear periods

Abstract

Suppose that F is a non-Archimedean local field of characteristic not 2 and D is a central division algebra over F. Let n be a positive integer. We show a classification modulo essentially square-integrable representations of standard modules of GLn(D) which have non-zero linear periods. By this classification, the conjecture of Prasad and Takloo-Bighash is reduced to the case of essentially square-integrable representations.