Invariant Cauchy-Riemann Operators and Relative Discrete Series of Line Bundles Over the Unit Ball of C~d

摘要

Let G/K be a Hermitian symmetric space realized as a bounded symmetric do- main. Shimeno [Sho] gives the Plancherel decomposition for the L~2-space of sec- tions of a homogeneous line bundle over G/K. It is proved that the discrete parts (also called relative discrete series) in the decomposition are all equivalent to holo- morphic discrete series. The proof involves identifying the infinitesimal charac- ters of the relative discrete series and those of the holomorphic discrete series.