Representations of SL(2)×G
نویسنده
چکیده
Let g be a complex reductive Lie algebra. We investigate a formalism for producing a natural model for representations of sl(2) × g which decompose in such a way so as to produce interesting correspondences between representations of sl(2) and of g. Our formalism generalizes the standard dual pair SL(2)× O(2n). We use it to obtain a formally unitary representation of sl(2,R)×u(3) that essentially realizes the symmetric square lift of Gelbart and Jacquet. We lift this representation of Lie algebras to a unitary representation of SL(2,R)× U(3) on a certain L2 space, with quite explicit formulas.
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