Period relations for Rankin–Selberg convolutions for {GL} (n) {GL} (n-1)

We formulate and prove the archimedean period relations for Rankin–Selberg convolutions for {GL} (n) {GL} (n-1). As a consequence, we prove the period relations for critical values of the Rankin–Selberg L-functions for {GL} (n) {GL} (n-1) over arbitrary number fields.