New \(R\)-matrices from representations of braid-monoid algebras based on superalgebras

DOI10.1016/j.nuclphysb.2005.10.025zbMath1192.82030arXivnlin/0509014OpenAlexW1981092391MaRDI QIDQ877310

N. E. Zubov

Publication date: 20 April 2007

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

Full work available at URL: https://arxiv.org/abs/nlin/0509014

zbMATH Keywords

integrable lattice modelstrigonometric solutionsgraded Yang--Baxter equationYang--Baxter equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (17)

Lax operator for the quantized orthosymplectic superalgebraU_q[osp(2|n)] ⋮ The continuum limit of \(a_{N - 1}^{(2)}\) spin chains ⋮ Dual description of \(\eta\)-deformed OSP sigma models ⋮ Exact solution and finite size properties of the \(U_{q}[\text{osp}(2| 2m)\) vertex models] ⋮ Reflection \(K\)-matrices for a nineteen vertex model with \(U_q [\operatorname{osp}(2 | 2)^{(2)}\) symmetry] ⋮ Reflection matrices for the \(U_q[sl(r|2m)^{(2)}\) vertex model] ⋮ Reflection matrices withU_q[osp⁽²⁾(2|2m) symmetry] ⋮ Phase diagram of an integrable alternating \(U_q[sl(2|1)\) superspin chain] ⋮ The staggered six-vertex model: conformal invariance and corrections to scaling ⋮ Reflection matrices for theU_q[spo(2n|2m) vertex model] ⋮ Reflection matrices for theU_q[osp(r|2m)⁽¹⁾ vertex model] ⋮ On the multiparametric ${\mathcal{U}}_{q}[{D}_{n+1}^{(2)}$ vertex model] ⋮ Non compact continuum limit of two coupled Potts models ⋮ Six-vertex model and non-linear differential equations. I: Spectral problem ⋮ On the \(\mathcal{{U}}_{q}[osp(1|2)\) Temperley-Lieb model] ⋮ Functional relations in nineteen-vertex models with domain-wall boundaries ⋮ On the critical behaviour of the integrable \(q\)-deformed \textit{OSp}(3|2) superspin chain

Cites Work

• Unnamed Item
• \(R\)-matrices and spectrum of vertex models based on superalgebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• The Kauffman polynomial of links and representation theory
• The algebraic Bethe ansatz for rational braid-monoid lattice models
• Solvable RSOS models based on the dilute BWM algebra
• Twisted quantum affine superalgebra \(U_q[\text{gl}(m|n)^{(2)}\) and new \(U_q[\text{osp}(m|n)]\) invariant \(R\)-matrices]
• Multiparameter quantum groups and twisted quasitriangular Hopf algebras
• Theory of braids
• BAXTERIZATION
• Graded solutions of the Yang-Baxter relation and link polynomials
• New solutions of Braid group representations associated with Yang–Baxter equation
• Solutions of the Yang-Baxter equation with extra nonadditive parameters. II. U_q(gl(m/n))
• Yang-Baxter algebras based on the two-colour BWM algebra
• U_qosp(2,2) lattice models
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem

This page was built for publication: New \(R\)-matrices from representations of braid-monoid algebras based on superalgebras