Standard Module Conjecture

Abstract

Let G be a quasi-split p-adic group. Under the assumption that the local coefficients $C_{\psi}$ defined with respect to $\psi $-generic tempered representations of standard Levi subgroups of G are regular in the negative Weyl chamber, we show that the standard module conjecture is true, which means that the Langlands quotient of a standard module is generic if and only if the standard module is irreducible.