Highest \(\ell\)-weight representations and functional relations

DOI10.3842/SIGMA.2017.043zbMath1419.17022arXiv1702.08710MaRDI QIDQ2360311

A. V. Razumov, Khazret S. Nirov

Publication date: 3 July 2017

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.08710

zbMATH Keywords

Verma modulesquantum loop algebras\(q\)-oscillatorshighest \(\ell\)-weight representations

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Yang-Baxter equations (16T25)

Related Items (2)

Quantum groups and functional relations for arbitrary rank ⋮ Vertex models and spin chains in formulas and pictures

Cites Work

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• Universal integrability objects
• Quantum groups and functional relations for lower rank
• On Drinfeld's realization of quantum affine algebras
• Drinfeld realization of affine quantum algebras: the relations
• Baxter's relations and spectra of quantum integrable models
• A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type \(A_ N\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Description of a class of projection operators for semisimple complex Lie algebras
• Quantum affine algebras
• The universal \(R\)-matrix for quantum untwisted affine Lie algebras
• A parametrization of compact groups
• Integrable structure of conformal field theory. II: \(Q\)-operator and DDV equation
• Integrable structure of conformal field theory. III: The Yang-Baxter relation
• Braid group action and quantum affine algebras
• Integrable light-cone lattice discretizations from the universal \(\text{R}\)-matrix
• Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
• From the Drinfeld realization to the Drinfeld-Jimbo presentation of affine quantum algebras: injectivity
• Finite type modules and Bethe ansatz for quantum toroidal \(\mathfrak{gl}_1\)
• Representations of quantum affinizations and fusion product
• Oscillator versus prefundamental representations
• Monodromy operators for higher rank
• Universal R-matrix and functional relations
• Exercises with the universalR-matrix
• Asymptotic representations and Drinfeld rational fractions
• Affinization of category $\mathcal {O}$ for quantum groups
• Quantum groups, Verma modules andq-oscillators: general linear case
• Oscillator versus prefundamental representations. II. Arbitrary higher ranks
• Drinfeld coproduct, quantum fusion tensor category and applications
• Quantum groups and functional relations for higher rank
• Integrable structure of \(W_3\) conformal field theory, quantum Boussinesq theory and boundary affine Toda theory

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