A Note on Iwasawa-Type Decomposition

We study the Iwasawa-type decomposition of an open subset of SL(n,ℂ) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on thespace of admissible elements in AN. We also show that the space of admissible elementsis a multiplicative subset of AN. We establish a geometric criterion: the symmetrizationof an admissible element maps the positive cone in ℂn into itself