The holomorphic discrete series of an affine symmetric space and representations with reproducing kernels
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- by G. Ólafsson and B. Ørsted PDF
- Trans. Amer. Math. Soc. 326 (1991), 385-405 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 326 (1991), 385-405
- MSC: Primary 22E46; Secondary 22E30, 43A85
- DOI: https://doi.org/10.1090/S0002-9947-1991-1002923-0
- MathSciNet review: 1002923