Completely \(\mathbb{Z}\) symmetric \(R\) matrix

DOI10.1007/BF00406551zbMath0771.17015OpenAlexW2070087591MaRDI QIDQ1196104

Youichi Shibukawa, Kimio Ueno

Publication date: 10 November 1992

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

Full work available at URL: https://doi.org/10.1007/bf00406551

zbMATH Keywords

quantum groupYang-Baxter equationinfinite-dimensional \(R\)-matrix

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (16)

Commuting difference operators arising from the elliptic C2(1)-face model ⋮ Elliptic K-matrix associated with Belavin's symmetric R-matrix ⋮ Vertex-IRF correspondence and factorized \(L\)-operators for an elliptic \(R\)-operator ⋮ Elliptic Ruijsenaars operators and functional equations ⋮ Topics in quantum integrable systems ⋮ Quantum Lax pairs via Dunkl and Cherednik operators ⋮ On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials ⋮ Simple construction of the elliptic boundary \(K\)-matrix ⋮ Integrability of a Hubbard-like model: lattice analogue of the \(\delta\)-function interacting gas ⋮ Boundary \(K\)-operator for the elliptic \(R\)-operator acting on functional space. ⋮ Generating functions for the coefficients of the Cremmer-Gervais \(R\)-matrices ⋮ Classification of R-operators ⋮ Ruijsenaars’ commuting difference operators and invariant subspace spanned by theta functions ⋮ Conserved operators of the generalized elliptic Ruijsenaars models ⋮ Nonlinear Schrödinger Model with Boundary, Integrability and Scattering Matrix Based on the Degenerate Affine Hecke Algebra ⋮ Nonstandard representations of type \(C\) affine Hecke algebra from \(K\)-operators.

Cites Work

• Unnamed Item
• Some algebraic structures connected with the Yang-Baxter equation
• Elliptic curves and soliton matrix differential equations
• Yang-Baxter equation and representation theory. I
• Cyclic \(L\)-operator related with a 3-state \(R\)-matrix
• Dynamical symmetry of integrable quantum systems
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Theta functions on Riemann surfaces
• Fusion procedure and Sklyanin algebra
• Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials

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