A simple construction of elliptic \(R\)-matrices

DOI10.1007/BF00739425zbMath0806.17020arXivhep-th/9402011OpenAlexW1487278211MaRDI QIDQ1338932

Vincent Pasquier, Giovanni Felder

Publication date: 20 December 1994

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

Full work available at URL: https://arxiv.org/abs/hep-th/9402011

zbMATH Keywords

quantum Yang-Baxter equationelliptic \(R\)-operator

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) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (12)

Elliptic K-matrix associated with Belavin's symmetric R-matrix ⋮ Vertex-IRF correspondence and factorized \(L\)-operators for an elliptic \(R\)-operator ⋮ Topics in quantum integrable systems ⋮ A new dynamical reflection algebra and related quantum integrable systems ⋮ 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 ⋮ 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 ⋮ Elliptic Dunkl operators, root systems, and functional equations ⋮ Nonstandard representations of type \(C\) affine Hecke algebra from \(K\)-operators.

Cites Work

• Embedded elliptic curves and the Yang-Baxter equations
• Dynamical symmetry of integrable quantum systems
• Unnamed Item

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