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 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.Comment: To appear in JF

The image of the heat kernel transform on Riemannian symmetric spaces of the noncompact type

The heat kernel or Bargmann-Segal transform on a noncompact Riemannian symmetric space X=G/K maps a square integrable function on X to a holomorphic function on the complex crown. In this article we determine the range of this transform.Comment: Expanded version. Two new sections added in order to clarify two remarks in the previous verson. 15

A Critique of Practice-Based Directives for Personal Relationship Law

Whether a liberal state should sanction marriages, and if so, in what form, is a hotly contested topic in liberal political theory. This essay responds to a radical proposal by Clare Chambers to end state sanctioned marriage and replace the institution with a network of practice-based directives aimed at ensuring gender equality and liberty. I argue that this proposed framework suffers from the serious defect of not only failing to ensure liberty but actively undermining it due to the way directives will inevitably either include too many people under their scope to preserve liberty or too few to ensure equality. While the presence of this defect does not settle the debate concerning how liberal states should handle marriage, it makes clearer the tradeoffs involved in selecting new personal relationship law frameworks to replace marriage