Unitary Representations on Partially Holomorphic Cohomology Spaces

Joseph Albert Wolf

1974年1月 · American Mathematical Soc.

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In "The Action of a Real Semisimple Lie group on a Complex Flag Manifold, I: Orbit Structure and Holomorphic Arc Components" we decomposed a complex flag manifold under the action of a real Lie group. At the end of the introduction, we described a program for using the real group orbits as the setting for geometric realization of unitary representations of semisimple groups. Here we carry out that program for reductive Lie groups, obtaining geometric realizations for the family of representations that is involved in the Plancherel formula.