International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 135167, 10 pages
doi:10.1155/2011/135167
Research Article

A Note on Iwasawa-Type Decomposition

1CEGEP, Champlain St. Lawrence, QC, G1V 4K2, Canada
2Department of Mathematics, The University of Arizona, Tucson, AZ 85721-0089, USA

Received 2 December 2010; Accepted 25 February 2011

Academic Editor: Hans Engler

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.

Abstract

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