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The holomorphic discrete series for affine symmetric spaces

By B. Rsted


Abstract. Consider a semisimple connected Lie group G with an affine symmetric space X. We study abstractly the intertwining operators from the discrete series of X into representations with reproducing kernel and, in particular, into the discrete series of G; each such is given by a convolution with an analytic function. For X of Hermitian type, we consider the holomorphic discrete series of X and here derive very explicit formulas for the intertwining operators. As a corollary we get a multiplicity one result for the series in question. The purpose of this work is twofold. The first is to study abstractly the intertwining operators between discrete series representations of an affine symmetric space X and discrete series of the corresponding semisimple group. The second is to obtain very explicit formulas for certain discrete representations o

Year: 1987
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