The explicit duality correspondence of (Sp(p,q),O∗(2n)

We investigate the type I dual pairs over the quaternion algebra H, namely the family of dual pairs (Sp(p,q),O∗(2n)). We give a complete and explicit description of duality correspondence for p+q⩽n as well as some of the cases for p+q>n, in terms of the Langlands parameters.