A note on Iwasawa-type decomposition (Q539334)

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