Cohomology classes, periods, and special values of Rankin-Selberg L-functions

In this article, we give a cohomological interpretation of (a special case of) the integrals constructed by the second named author and Q. Zhang {YanZhang2023} which represent the product of Rankin-Selberg L-functions of GLₙₘ and GLₙₙ₋ₘ₋₁ for $m<n$. As an application, we prove an algebraicity result for the special values of certain L-functions. This work is a generalization of the algebraicity result of Raghuram for GLₙₙ₋₁ {Raghuram2010} in the special case $m=n-1$, and the results of Mahnkopf {Mahnkopf1998, Mahnkopf2005} in the special case $m=n-2$.