Formal Dimension for Semisimple Symmetric Spaces

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