Uniqueness of higher Gaudin Hamiltonians

DOI10.1016/S0034-4877(08)80013-4zbMath1178.17012arXivmath/0608588MaRDI QIDQ1025375

Leonid Rybnikov

Publication date: 18 June 2009

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608588

zbMATH Keywords

semisimple Lie algebrasGaudin model

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine sl2 Gaudin model ⋮ Symmetrisation and the Feigin–Frenkel centre ⋮ Opers with irregular singularity and spectra of the shift of argument subalgebra ⋮ Gaudin algebras, RSK and Calogero–Moser cells in Type A ⋮ Feigin-Frenkel center in types \(B\), \(C\) and \(D\) ⋮ Perfect integrability and Gaudin models ⋮ Limits of Gaudin algebras, quantization of bending flows, Jucys-Murphy elements and Gelfand-Tsetlin bases ⋮ On classical limits of Bethe subalgebras in Yangians ⋮ Gaudin models for 𝔤𝔩(m|n) ⋮ A bi-Hamiltonian nature of the Gaudin algebras

Cites Work

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• Gaudin model, Bethe ansatz and critical level
• Hitchin systems, higher Gaudin operators and \(R\)-matrices
• Wakimoto modules, opers and the center at the critical level
• The quantum Gaudin system
• Centralizers of certain quadratic elements in Poisson-Lie algebras and the method of translation of invariants
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
• Lie Group Representations on Polynomial Rings

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