Archimedean period relations for Rankin-Selberg convolutions

TL;DR

This paper establishes archimedean period relations for Rankin-Selberg convolutions of GL(n) groups, proving non-vanishing of associated modular symbols and extending previous results to all generic cohomological representations.

Contribution

It formulates and proves archimedean period relations for a broad class of Rankin-Selberg convolutions, generalizing earlier tempered cases.

Findings

Proved archimedean period relations for GL(n)×GL(n) and GL(n)×GL(n-1).

Established non-vanishing of archimedean modular symbols.

Extended results to all generic cohomological representations.

Abstract

We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of $\text{GL}(n)\times \text{GL}(n)$ and $\text{GL}(n)\times \text{GL}(n-1)$, for all generic cohomological representations. As a consequence, we prove the non-vanishing of the archimedean modular symbols. This extends the earlier results in [LLS24] for essentially tempered representations of $\text{GL}(n)\times\text{GL}(n-1)$.