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The holomorphic discrete series of an affine symmetric space and representations with reproducing kernels

Authors: G. Ólafsson and B. Ørsted
Journal: Trans. Amer. Math. Soc. 326 (1991), 385-405
MSC: Primary 22E46; Secondary 22E30, 43A85
MathSciNet review: 1002923
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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.

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