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Mathematics, Representation Theory
Abstract:
For a real bounded symmetric domain, G/K, we construct various natural
enlargements to which several aspects of harmonic analysis on G/K and G have
extensions. Our starting point is the realization of G/K as a totally real
submanifold in a bounded domain G_h/K_h. We describe the boundary orbits and
relate them to the boundary orbits of G_h/K_h. We relate the crown and the
split-holomorphic crown of G/K to the crown \Xi_h of G_h/K_h. We identify an
extension of a representation of K to a larger group L_c and use that to extend
sections of vector bundles over the Borel compactification of G/K to its
closure. Also, we show there is an analytic extension of K-finite matrix
coefficients of G to a specific Matsuki cycle space.
