Towards trigonometric deformation of sl^2 coset VOA

DOI10.1063/1.5081799zbMath1416.81093arXiv1811.02056OpenAlexW3106304422MaRDI QIDQ5228084

Michio Jimbo, Boris L. Feigin, Evgenii E. Mukhin

Publication date: 8 August 2019

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

Full work available at URL: https://arxiv.org/abs/1811.02056

zbMATH Keywords

bosonization technique

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items

Combinatorics of vertex operators and deformed \(W\)-algebra of type D\((2,1;\alpha)\), Shuffle algebra realization of quantum affine superalgebra \(U_v( \widehat{\mathfrak{D}}(2, 1; \theta))\), Integrable sigma models at RG fixed points: quantisation as affine Gaudin models, Commutative subalgebra of a shuffle algebra associated with quantum toroidal \(\mathfrak{gl}_{m|n}\), Quantum toroidal algebra associated with \(\mathfrak{gl}_{m|n}\), Evaluation modules for quantum toroidal \(\mathfrak{gl}_n\) algebras, A note on quiver quantum toroidal algebra, Shifted quiver quantum toroidal algebra and subcrystal representations

Cites Work

• Unnamed Item
• Unnamed Item
• Integrable structure of quantum field theory: classical flat connections versus quantum stationary states
• Fock representations of the affine Lie algebra \(A_ 1^{(1)}\)
• The ${(\mathfrak{gl}_{m},\mathfrak{gl}_{n})}$ duality in the quantum toroidal setting
• Quantum transfer-matrices for the sausage model
• Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
• The sigma model (dual) representation for a two-parameter family of integrable quantum field theories
• Finite type modules and Bethe ansatz for quantum toroidal \(\mathfrak{gl}_1\)
• Integrable boundary interaction in 3D target space: the ``pillow-brane model
• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• Integrals of motion from quantum toroidal algebras
• Toroidal and level 0 Uq′(sln+1∧) actions on Uq(gln+1∧) modules
• Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz
• The \(\widehat{s\ell}(2)\oplus\widehat{s\ell}(2)/\widehat{s\ell}(2)\) coset theory as a Hamiltonian reduction of \(\widehat{D}(2|1;\alpha)\)