The orbit structure of the Gelfand-Zeitlin group on n x n matrices

Details The orbit structure of the Gelfand-Zeitlin group on n x n matrices The orbit structure of the Gelfand-Zeitlin group on n x n matrices

2008-11-09

arxiv.org/abs/0811.1351v2

Mathematics

Symplectic Geometry

30 pages: Version 2 contains a stronger result in section 5.3 (Theorem 5.15)

Scientific paper

In recent work (\cite{KW1},\cite{KW2}), Kostant and Wallach construct an action of a simply connected Lie group $A\simeq \mathbb{C}^{{n\choose 2}}$ on $gl(n)$ using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In \cite{KW1}, the authors show that $A$-orbits of dimension ${n\choose 2}$ form Lagrangian submanifolds of regular adjoint orbits in $gl(n)$. They describe the orbit structure of $A$ on a certain Zariski open subset of regular semisimple elements. In this paper, we describe all $A$-orbits of dimension ${n\choose 2}$ and thus all polarizations of regular adjoint orbits obtained using Gelfand-Zeitlin theory.

Affiliated with

Also associated with

No associations

Rating

The orbit structure of the Gelfand-Zeitlin group on n x n matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The orbit structure of the Gelfand-Zeitlin group on n x n matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The orbit structure of the Gelfand-Zeitlin group on n x n matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484060