Thu 2 Feb 2006
Philip Foth and I have written about quaternion flag manifolds in the paper
where we describe certain natural 4-vector fields on quaternionic flag manifolds.
These vector fields geometrically determine the Bruhat cell decomposition. These structures naturally descend from the symplectic group , and are related to the dressing action given by the Iwasawa decomposition of the general linear group over the quaternions,
.
This paper was published in Communications in Mathematical Physics (238) 2003, pages 119-129.



