The geometry of flag manifold and holomorphic extension of Szegö kernels for SU(p,q)

L. Barchini, S.G. Gindikin and H.W. Wong

Vol. 179 (1997), No. 2, 201–220

DOI: 10.2140/pjm.1997.179.201

Abstract

Let G₀ = SU(p,q), K₀ = S(U(p) × U(q)) a maximal compact subgroup, and let G,K be their complexifications. Finally, let B be a Borel subgroup of G. We define a number of algebraic functions on G∕B × G∕K and use them to construct a Stein extension of the Riemannian symmetric space G₀∕K₀. These functions capture the singularities that can occur in the meromorphic extensions of the Knapp-Wallach Szegö kernels. These facts imply that all solutions of the Schmid equations extend holomorphically to the space of linear cycles.

Milestones

Received: 22 September 1995

Revised: 21 March 1996

Published: 1 June 1997