Period relations for Rankin-Selberg convolutions for $\mathrm{G}\mathrm{L}(n)\times \mathrm{G}\mathrm{L}(n)$

In this paper, we study the special values of Rankin-Selberg L-functions as a continuation of [LLS24]. Utilizing the modular symbol approach, we prove the rationality and period relations for some critical values of Rankin-Selberg L-functions for $\mathrm{G}\mathrm{L}(n)\times \mathrm{G}\mathrm{L}(n)$ over any number field that contains a CM field.