Eigendistributions for Orthogonal Groups and Representations of Symplectic Groups
نویسندگان
چکیده
We consider the action of H = O(p, q) on the matrix space Mp+q,n(R). We study a certain orbit O of H in the null cone N ⊆ Mp+q,n(R) which supports an eigendistribution dνO for H . Using some identities of Capelli type developed in the Appendix, we determine the structure of G̃ = Sp(2n,R)∼-cyclic module generated by dνO under the oscillator representation of G̃ (the metaplectic cover of G = Sp(2n(p + q),R)). Applications to local theta correspondence and a generalized Huygens’ Principle are given.
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