Gaudin models for 𝔤𝔩(m|n)

DOI10.1063/1.4919652zbMath1394.17065arXiv1404.3526OpenAlexW1573280746MaRDI QIDQ5253069

Charles A. S. Young, Evgenii E. Mukhin, Benoît Vicedo

Publication date: 4 June 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.3526

zbMATH Keywords

Bethe ansatzGaudin model, Lie superalgebra

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Applications of Lie algebras and superalgebras to integrable systems (17B80) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (12)

Completeness of Wronskian Bethe equations for rational \(\mathfrak{gl}_{\mathsf{m}|\mathsf{n}}\) spin chains ⋮ Cyclotomic Gaudin models: construction and Bethe ansatz ⋮ Completeness of Bethe ansatz for Gaudin models associated with \(\mathfrak{gl}(1|1)\) ⋮ Solutions of $ \newcommand{\g}{\mathfrak{g}} \newcommand{\n}{\mathfrak{n}} \newcommand{\gl}{\mathfrak{gl}} \gl_{m|n}$ XXX Bethe ansatz equation and rational difference operators ⋮ On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains ⋮ Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras ⋮ Gaudin model and Deligne's category ⋮ The duality of \(\mathfrak{gl}_{m | n}\) and \(\mathfrak{gl}_k\) Gaudin models ⋮ New compact construction of eigenstates for supersymmetric spin chains ⋮ Bethe ansatz equations for orthosymplectic Lie superalgebras and self-dual superspaces ⋮ On the Gaudin model associated to Lie algebras of classical types ⋮ The solutions of \(\mathfrak{gl}_{M|N}\) Bethe ansatz equation and rational pseudodifferential operators

Cites Work

• Opers with irregular singularity and spectra of the shift of argument subalgebra
• Uniqueness of higher Gaudin Hamiltonians
• Arrangements of hyperplanes and Lie algebra homology
• Gaudin model, Bethe ansatz and critical level
• The quantum Gaudin system
• Gaudin models with irregular singularities
• OFF-SHELL BETHE ANSATZ EQUATION FOR GAUDIN MAGNETS AND SOLUTIONS OF KNIZHNIK-ZAMOLODCHIKOV EQUATIONS
• The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for $\widehat{\mathfrak{gl}}(m|n)$
• Schubert calculus and representations of the general linear group
• The nested Bethe ansatz for ‘all’ closed spin chains
• CRITICAL POINTS OF MASTER FUNCTIONS AND FLAG VARIETIES
• The Kac Construction of the Centre of U(g) for Lie Superalgebras
• Bethe eigenvectors of higher transfer matrices
• On the number of populations of critical points of master functions
• Norm of a Bethe vector and the Hessian of the master function
• Bethe vectors of the \(\text{osp}(1\mid 2)\) Gaudin model
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