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

TL;DR

This paper explores a motivic interpretation of Whittaker periods for automorphic representations of GL_n, relating them to Yoshida's fundamental periods under certain number field conditions.

Contribution

It provides a new motivic perspective on Whittaker periods, connecting them explicitly to Yoshida's fundamental periods for specific base fields.

Findings

Expressed Whittaker periods in terms of Yoshida's fundamental periods

Established relations for totally real and CM fields

Bridged automorphic periods with motivic conjectures

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.