In this thesis I will describe the theta correspondence for the reductive dual pairs (Sp(p,q),O^*(4)) in terms of Langlands parameters. For the general reductive dual pairs (Sp(p,q),O^*(2n)), the explicit theta correspondence has been given in [21] for the case p + q ≤ n. So in this thesis we only need to consider the case p + q > 2. The main techniques used in this thesis are the correspondence in joint harmonic space and induction principle. The induction principle was first observed by Rallis and further developed by Moeglin. Combined with the result of correspondence on infinitesimal characters by Przebinda, I could give the explicit Howe correspondence for reductive dual pairs (Sp(p,q),O^*(4)) in terms of Langlands parameters for almost cases....[ Read more ]

In this thesis I will describe the theta correspondence for the reductive dual pairs (Sp(p,q),O^*(4)) in terms of Langlands parameters. For the general reductive dual pairs (Sp(p,q),O^*(2n)), the explicit theta correspondence has been given in [21] for the case p + q ≤ n. So in this thesis we only need to consider the case p + q > 2. The main techniques used in this thesis are the correspondence in joint harmonic space and induction principle. The induction principle was first observed by Rallis and further developed by Moeglin. Combined with the result of correspondence on infinitesimal characters by Przebinda, I could give the explicit Howe correspondence for reductive dual pairs (Sp(p,q),O^*(4)) in terms of Langlands parameters for almost cases.