Classification of standard modules with linear periods

Abstract

Suppose that $F$ is a non-Archimedean local field 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 ${\mathrm{GL}}_n(D)$ 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.

to appear in J. Number Theory

References in corpus (1)

• Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations