Periods of residual representations of SO\((2l)\) (Q1434146)

From authors' abstract: ``We extend results on G\(_2\)-period of residual representations of SO\(_8\) to a generalized G\(_2\)-period of residual representations of SO\(_{2\ell}\) \((\ell\geq 4)\). The period is expected to detect the nonvanishing of the relevant tensor product L-function at the center of symmetry, which is a special case of the Gross-Prasad conjecture. More general cases will be considered later.'' The paper consists of matrix decompositions and integration.