The Gelfand–Zeitlin integrable system and K-orbits on the flag variety

DOI10.1007/978-1-4939-1590-3_5zbMath1329.14095arXiv1111.2868OpenAlexW1596831379MaRDI QIDQ5250231

Sam Evens, Mark Colarusso

Publication date: 19 May 2015

Published in: Symmetry: Representation Theory and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2868

zbMATH Keywords

integrable systemsflag varietynilpotent matricessymmetric subgroupGelfand-Zeitlin theory

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (12)

Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag varieties ⋮ \(B_{n -1}\)-bundles on the flag variety. II ⋮ Gelfand-Tsetlin modules of quantum \(\mathfrak{gl}_n\) defined by admissible sets of relations ⋮ On the fibres of Mishchenko-Fomenko systems ⋮ Combinatorial construction of Gelfand-Tsetlin modules for \(\mathfrak{gl}_n\) ⋮ Eigenvalue coincidences and \(K\)-orbits. I ⋮ Irreducible subquotients of generic Gelfand-Tsetlin modules over \(U_q(\mathfrak{gl}_n)\) ⋮ Explicit construction of irreducible modules for \(U_q(\mathfrak{gl}_n)\) ⋮ Geometric construction of Gelfand-Tsetlin modules over simple Lie algebras ⋮ Principal Galois orders and Gelfand-Zeitlin modules ⋮ Gelfand-Tsetlin modules of 𝔰𝔩(3) in the principal block ⋮ \(B_{n -1}\)-bundles on the flag variety. I

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