The orbit structure of the Gelfand-Zeitlin group on \(n\times n\) matrices

DOI10.2140/PJM.2011.250.109zbMath1218.14039arXiv0811.1351OpenAlexW2963788680MaRDI QIDQ627417

Mark Colarusso

Publication date: 1 March 2011

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.1351

zbMATH Keywords

enveloping algebraintegrable systemLagrangian submanifoldLie-Poisson structurealgebraic group actionsGelfand-Zeitlin algebra

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Group actions on affine varieties (14R20)

Related Items (5)

\(K\)-orbits on the flag variety and strongly regular nilpotent matrices ⋮ Lie-Poisson theory for direct limit Lie algebras ⋮ Eigenvalue coincidences and \(K\)-orbits. I ⋮ Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\) ⋮ On algebraic integrability of Gelfand-Zeitlin fields

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