CAP representations of inner forms of Sp ( 4 ) with respect to Klingen parabolic subgroup Takanori Yasuda
نویسنده
چکیده
The unitary group of the hyperbolic hermitian space of dimension two over a quaternion division algebra over a number field is a non-quasisplit inner form of Sp(4), and does not have a parabolic subgroup corresponding to the Klingen parabolic subgroup. However, it has CAP representations with respect to the Klingen parabolic subgroup. We construct them by using the theta lifting from the unitary groups of one-dimensional (-1)-hermitian spaces and estimate their multiplicities in the discrete spectrum. In many cases, their multiplicities become bigger than 1.
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