Rankin-Selberg integrals for principal series representations of GL(n)

TL;DR

This paper proves that local Rankin--Selberg integrals for principal series representations of GL(n) match simpler subgroup integrals, with differences only by known gamma factors, simplifying their computation.

Contribution

It establishes a direct equivalence between complex Rankin--Selberg integrals and simpler subgroup integrals for principal series representations of GL(n).

Findings

Integral equivalence up to gamma factors

Simplification of Rankin--Selberg integral computations

Enhanced understanding of local factors in automorphic forms

Abstract

We prove that the local Rankin--Selberg integrals for principal series representations of the general linear groups agree with certain simple integrals over the Rankin--Selberg subgroups, up to certain constants given by the local gamma factors.