Oscillator realisations associated to the \(D\)-type Yangian: towards the operatorial Q-system of orthogonal spin chains

DOI10.1016/J.NUCLPHYSB.2020.115063zbMath1479.82015arXiv2001.06825OpenAlexW3028762372MaRDI QIDQ2230502

Rouven Frassek

Publication date: 17 September 2021

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06825

zbMATH Keywords

Yang-Baxter equationsorthogonal spin chains

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items (10)

Rational Lax matrices from antidominantly shifted extended Yangians: BCD types ⋮ On exceptional 't Hooft lines in 4D-Chern-Simons theory ⋮ Minuscule ABCDE Lax operators from 4D Chern-Simons theory ⋮ Transfer matrices of rational spin chains via novel BGG-type resolutions ⋮ Embedding integrable superspin chain in string theory ⋮ Universal Baxter TQ-relations for open boundary quantum integrable systems ⋮ Representations of orthogonal and symplectic Yangians ⋮ Orthosymplectic superoscillator Lax matrices ⋮ Lax operator and superspin chains from 4D CS gauge theory ⋮ Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin

Cites Work

• Unnamed Item
• Q-operators for the open Heisenberg spin chain
• Orthogonal and symplectic Yangians and Yang-Baxter \(R\)-operators
• Conformal algebra: R-matrix and star-triangle relation
• Baxter's Q-operators and operatorial Bäcklund flow for quantum (super)-spin chains
• Baxter Q-operators and representations of Yangians
• On the \(R\)-matrix realization of Yangians and their representations
• Baxter's relations and spectra of quantum integrable models
• Baxter's Q-operators for supersymmetric spin chains
• Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras
• Integrable structure of conformal field theory. III: The Yang-Baxter relation
• Orthogonal and symplectic Yangians: linear and quadratic evaluations
• Second-order evaluations of orthogonal and symplectic Yangians
• Asymptotic representations of augmented \(q\)-Onsager algebra and boundary \(K\)-operators related to Baxter Q-operators
• A family of \(\mathrm{GL}_r\) multiplicative Higgs bundles on rational base
• A note on \(q\)-oscillator realizations of \(U_q(gl(M|N))\) for Baxter \(Q\)-operators
• Quantum geometry and quiver gauge theories
• Baxter operators and Hamiltonians for ``nearly all integrable closed \(gl(n\)) spin chains
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case
• Coulomb branches of \(3d\) \(\mathcal{N}=4\) quiver gauge theories and slices in the affine Grassmannian
• Oscillator versus prefundamental representations
• The spinorialR-matrix
• Asymptotic representations and Drinfeld rational fractions
• Lie Groups and Lie Algebras for Physicists
• On diagonal solutions of the reflection equation
• Oscillator versus prefundamental representations. II. Arbitrary higher ranks
• Algebraic Bethe ansatz forQ-operators: the Heisenberg spin chain
• The ODE/IM correspondence

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