A Note on Iwasawa-Type Decomposition

We study the Iwasawa-type decomposition of an open subset of SL(,？) as SU(,). We show that the dressing action of SU(,) is globally defined on the space of admissible elements in . We also show that the space of admissible elements is a multiplicative subset of . We establish a geometric criterion: the symmetrization of an admissible element maps the positive cone in ？ into itself.