Extensions of real bounded symmetric domains
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 Gh/Kh. We describe the boundary orbits and relate them to the boundary orbits of Gh/Kh. We relate the crown and the split-holomorphic crown of G/K to the crown Ξh of Gh/Kh. We identify an extension of a representation of K to a larger group Lc 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.
Publication Source (Journal or Book title)
Journal of Functional Analysis
Ólafsson, G., & Stanton, R. (2020). Extensions of real bounded symmetric domains. Journal of Functional Analysis, 279 (8) https://doi.org/10.1016/j.jfa.2020.108709