Unitary Representations and Heisenberg Parabolic Subgroup
نویسنده
چکیده
In this paper, we study the restriction of an irreducible unitary representation π of the universal covering S̃p2n(R) to a Heisenberg maximal parabolic group P̃ . We prove that if π|P̃ is irreducible, then π must be a highest weight module or a lowest weight module. This is in sharp constrast with the GLn(R) case. In addition, we show that for a unitary highest or lowest weight module, π|P̃ decomposes discretely. We also treat the groups U(p, q) and O ∗(2n).
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