Archimedean period relations and period relations for Rankin-Selberg convolutions

We prove the Archimedean period relations for Rankin-Selberg convolutions for $mathrm{GL}(n)times mathrm{GL}(n-1)$. This implies the period relations for critical values of the Rankin-Selberg L-functions for $mathrm{GL}(n)times mathrm{GL}(n-1)$.