Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers (Q1671025)

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English	Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers	scientific article

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scholarly article

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Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers (English)

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zbMATH Open document ID

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10.1007/s00220-018-3194-9

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David Hernandez

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Edward V. Frenkel'

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Communications in Mathematical Physics

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publication date

6 September 2018

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full work available at URL

https://arxiv.org/abs/1606.05301

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Mathematics Subject Classification ID

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zbMATH DE Number

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MaRDI profile type

MaRDI publication profile

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Integrable structure of \(W_3\) conformal field theory, quantum Boussinesq theory and boundary affine Toda theory

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Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz

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Integrable structure of conformal field theory. II: \(Q\)-operator and DDV equation

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Integrable structure of conformal field theory. III: The Yang-Baxter relation

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Spectral determinants for Schrödinger equation and \({\mathbb{Q}}\)-operators of conformal field theory

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Higher-level eigenvalues of \(Q\)-operators and Schrödinger equation

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Baxter Q-operators and representations of Yangians

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Restricted solid-on-solid models connected with simply laced algebras and conformal field theory

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Braid group action and quantum affine algebras

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Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case

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Beyond Kirillov-Reshetikhin modules

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Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras

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Differential equations for general<i>SU</i>(<i>n</i>) Bethe ansatz systems

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The ODE/IM correspondence

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Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations

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On the relation between Stokes multipliers and the \(T\)-\(Q\) systems of conformal field theory

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Lie algebras and equations of Korteweg-de Vries type

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Representations of affine Kac-Moody algebras, bosonization and resolutions

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Quantization of the Drinfel'd-Sokolov reduction.

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AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS

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Smallness problem for quantum affine algebras and quiver varieties

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Quantization of soliton systems and Langlands duality

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Gaudin model, Bethe ansatz and critical level

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Gaudin models with irregular singularities

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Finite type modules and Bethe ansatz for quantum toroidal \(\mathfrak{gl}_1\)

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A rigid irregular connection on the projective line

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Baxter's relations and spectra of quantum integrable models

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Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras.

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Gerbal Representations of Double Loop Groups

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The Kirillov-Reshetikhin conjecture and solutions of T-systems

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On minimal affinizations of representations of quantum groups

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Kirillov-Reshetikhin Conjecture: The General Case

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Asymptotic representations and Drinfeld rational fractions

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Cluster algebras and quantum affine algebras

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Cluster algebras and category \(\mathcal O\) for representations of Borel subalgebras of quantum affine algebras

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Periodicities of T-systems and Y-systems

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Baxter's<i>Q</i>-operator for the<i>W</i>-algebra<i>W<sub>N</sub></i>

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Analytic Bethe ansatz for fundamental representations of Yangians

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Functional relations and analytic Bethe ansatz for twisted quantum affine algebras

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Quantum loop algebras, quiver varieties, and cluster algebras

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Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case

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Quantum geometry and quiver gauge theories

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The spectrum of the transfer matrices connected with Kac-Moody algebras

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Polynomial relations for \(q\)-characters via the ODE/IM correspondence

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