THESIS
2014
Abstract
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....[
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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.
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