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

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dc.creatorColarusso, Mark
dc.date2008-11-09
dc.date2009-03-31
dc.date.accessioned2026-07-07T12:58:01Z
dc.date.available2026-07-07T12:58:01Z
dc.descriptionIn 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.
dc.description30 pages: Version 2 contains a stronger result in section 5.3 (Theorem 5.15)
dc.identifierhttps://arxiv.org/abs/0811.1351
dc.identifierhttp://arxiv.org/abs/0811.1351
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225103
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Geometry
dc.subject14L30; 14R20; 37J35; 53D17
dc.titleThe orbit structure of the Gelfand-Zeitlin group on n x n matrices
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