Journal of Lie Theory Volume 6 (1996) 191-206 ◯^{C} 1996 Heldermann Verlag

Determinant Functions and the Geometry of the Flag Manifold for SU(p,q)

L. Barchini, S. G. Gindikin^{∗}, H. W. Wong

Communicated by J. Hilgert

Abstract. Let G_{0} = SU(p, q) with q ≤ p, K_{0} = 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 describe the closures of codimension one K orbits of the flag manifold G/B. We show how the underlying geometry of the flag manifold interacts with these functions. In particular, we shall use these functions to construct a Stein extension of the Riemannian symmetric space G_{0}/K_{0} , whose connected component turns out to be the space of linear cycles in most cases.

Department of Mathematics Temple University Broad and Montgomery Philadelphia PA 19122 Department of Mathematics Rutgers University New Brunswick NJ 08903

Received March 22, 1996 and in final form July 18, 1996

∗Supported by NSF DMS 9202049.

ISSN 0949–5932 / $2.50 ◯^{C} Heldermann Verlag