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