An invariant theory approach for the unramified computation of Rankin–Selberg integrals for quasi-split SO2n×GLn

We compute the local integral, with unramified data, derived from the global Rankin–Selberg integral for SO2n×GLn, where SO2n is a quasi-split orthogonal group in 2n variables over a number field. Our unramified computation is achieved by a new approach that uses Schur polynomials and a branching rule.