A motivic interpretation of Whittaker periods for ${\mathrm{GL}}_n$

Abstract

Admitting the existence of conjectural motives attached to cohomological irreducible cuspidal automorphic representations of ${\mathrm{GL}}_n$, we write down Raghuram and Shahidi's Whittaker periods in terms of Yoshida's fundamental periods when the base field is a totally real number field or a CM field.