Eigenvalues of Bethe vectors in the Gaudin model

DOI10.1134/S0040577917090021zbMath1382.81100arXiv1506.01884OpenAlexW2962806247WikidataQ64433300 ScholiaQ64433300MaRDI QIDQ681945

Evgenii E. Mukhin, Alexander I. Molev

Publication date: 13 February 2018

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01884

zbMATH Keywords

\(q\)-characterBethe vectorclassical \(W\)-algebraGaudin Hamiltonian

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Vertex operators; vertex operator algebras and related structures (17B69) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Bethe-Salpeter and other integral equations arising in quantum theory (81Q40)

Related Items (7)

Segal-Sugawara vectors for the Lie algebra of type \(G_2\) ⋮ Center of the quantum affine vertex algebra in type \(A\) ⋮ Equivalences between three presentations of orthogonal and symplectic Yangians ⋮ The \(R\)-matrix presentation for the Yangian of a simple Lie algebra ⋮ Lower bounds for numbers of real self-dual spaces in problems of Schubert calculus ⋮ Bethe ansatz equations for orthosymplectic Lie superalgebras and self-dual superspaces ⋮ On the Gaudin model associated to Lie algebras of classical types

Uses Software

• QuantumMACMAHON

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Opers with irregular singularity and spectra of the shift of argument subalgebra
• Algebraic properties of Manin matrices. I
• On the \(R\)-matrix realization of Yangians and their representations
• The argument shift method and the Gaudin model
• KZ equation, G-opers, quantum Drinfeld-Sokolov reduction, and quantum Cayley-Hamilton identity
• Arrangements of hyperplanes and Lie algebra homology
• Gaudin model, Bethe ansatz and critical level
• Feigin-Frenkel center in types \(B\), \(C\) and \(D\)
• Classical \(\mathcal W\)-algebras in types \(A\), \(B\), \(C\), \(D\) and \(G\)
• 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 $\widehat{\mathfrak{gl}}(m|n)$
• Yangian Characters and Classical $$\mathcal{W}$$ -Algebras
• Paths, tableaux andq-characters of quantum affine algebras: theC_ncase
• On Higher-Order Sugawara Operators
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
• CRITICAL POINTS OF MASTER FUNCTIONS AND FLAG VARIETIES
• A new formula for Pfaffian-type Segal-Sugawara vector
• Bethe eigenvectors of higher transfer matrices
• The quantum MacMahon Master Theorem
• Norm of a Bethe vector and the Hessian of the master function
• Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras.

This page was built for publication: Eigenvalues of Bethe vectors in the Gaudin model