The Plancherel formula for line bundles on complex hyperbolic spaces

AbstractIn this paper we obtain the Plancherel formula for the spaces of L2-sections of line bundles over the complex projective hyperboloids G/H with G=U(p,q;C) and H=U(1;C)×U(p−1,q;C). The Plancherel formula is given in an explicit form by means of spherical distributions associated with a character χ of the subgroup H. We obtain the Plancherel formula by a special method which is also suitable for other problems, for example, for quantization in the spirit of Berezin