If G is a semisimple Lie group and (pi, H) an irreducible unitary representation of G with square integrable matrix coefficients, then there exists a number d>(pi) such that (For Allv', w, w' is an element of H) 1/d(pi) = integral (G) d mu (G)(g). The constant d(pi) is called the formal dimension of (pi, H) and was computed by Harish-Chandra in HC56, 66. If now H G is a semisimple symmetric space and (pi, H) an irreducible H-spherical unitary (pi, H) belonging to the holomorphic discrete series of HG, then one can define a formal dimension d(pi) in an analogous manner. In this paper we compute d(pi) for these classes of representations. References: 45
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