On algebraic integrability of Gelfand-Zeitlin fields

DOI10.1007/s00031-010-9082-9zbMath1211.14053arXiv0908.3879OpenAlexW2085304783MaRDI QIDQ969616

Sam Evens, Mark Colarusso

Publication date: 7 May 2010

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.3879

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)

Related Items (7)

\(K\)-orbits on the flag variety and strongly regular nilpotent matrices ⋮ Lie-Poisson theory for direct limit Lie algebras ⋮ Gelfand-Tsetlin modules of quantum \(\mathfrak{gl}_n\) defined by admissible sets of relations ⋮ Combinatorial construction of Gelfand-Tsetlin modules for \(\mathfrak{gl}_n\) ⋮ Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\) ⋮ Explicit construction of irreducible modules for \(U_q(\mathfrak{gl}_n)\) ⋮ Gelfand-Tsetlin modules of 𝔰𝔩(3) in the principal block

Cites Work

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• The orbit structure of the Gelfand-Zeitlin group on \(n\times n\) matrices
• Gelfand-Zeitlin actions and rational maps
• Hamiltonian group actions and dynamical systems of calogero type
• Decomposition Varieties in Semisimple Lie Algebras
• Lie Group Representations on Polynomial Rings

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