Copyright © 2011 Philip Foth. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.