The argument shift method and the Gaudin model

DOI10.1007/s10688-006-0030-3zbMath1112.17018arXivmath/0606380OpenAlexW2084967443MaRDI QIDQ883625

Leonid Rybnikov

Publication date: 5 June 2007

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606380

zbMATH Keywords

Gaudin modelaffine Kac-Moody algebracritical levelargument shift methodMishchenko-Fomenko subalgebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Poisson algebras (17B63)

Related Items (36)

Segal-Sugawara vectors for the Lie algebra of type \(G_2\) ⋮ On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level ⋮ Higher Sugawara operators for the quantum affine algebras of type \(A\) ⋮ A remark on Mishchenko-Fomenko algebras and regular sequences ⋮ Symmetrisation and the Feigin–Frenkel centre ⋮ Gaudin models with irregular singularities ⋮ Finite-dimensional integrable systems: a collection of research problems ⋮ Cyclotomic Gaudin models with irregular singularities ⋮ Quantizing Mishchenko–Fomenko subalgebras for centralizers via affine $W$-algebras ⋮ Quantization of the shift of argument subalgebras in type \(A\) ⋮ Folded quantum integrable models and deformed \(W\)-algebras ⋮ Opers with irregular singularity and spectra of the shift of argument subalgebra ⋮ Center of the quantum affine vertex algebra in type \(A\) ⋮ Quasi-derivations on 𝑈𝔤𝔩_{𝔫} and the argument shift method ⋮ On maximal commutative subalgebras of Poisson algebras associated with involutions of semisimple Lie algebras ⋮ Gaudin algebras, RSK and Calogero–Moser cells in Type A ⋮ Affine Gaudin models and hypergeometric functions on affine opers ⋮ Shift of argument algebras and de Concini–Procesi spaces ⋮ Automorphisms of finite order, periodic contractions, and Poisson-commutative subalgebras of \({\mathcal{S}}(\mathfrak{g})\) ⋮ The argument shift method in universal enveloping algebra \(U \mathfrak{gl}_d\) ⋮ Feigin-Frenkel center in types \(B\), \(C\) and \(D\) ⋮ Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces ⋮ Integrable Systems, Shuffle Algebras, and Bethe Equations ⋮ Center at the critical level for centralizers in type \(A\) ⋮ Crystals and monodromy of Bethe vectors ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Perfect integrability and Gaudin models ⋮ Generalized Gaudin systems in an external magnetic field and reflection equation algebras ⋮ Degeneration of Bethe subalgebras in the Yangian of \(\mathfrak {gl}_n\) ⋮ Eigenvalues of Bethe vectors in the Gaudin model ⋮ \((\mathfrak{gl}_M, \mathfrak{gl}_N)\)-dualities in Gaudin models with irregular singularities ⋮ Limits of Gaudin algebras, quantization of bending flows, Jucys-Murphy elements and Gelfand-Tsetlin bases ⋮ On classical limits of Bethe subalgebras in Yangians ⋮ Periodic automorphisms, compatible Poisson brackets, and Gaudin subalgebras ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Spectra of Bethe subalgebras of \(Y(\mathfrak{gl}_n)\) in tame representations

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