Embedded elliptic curves and the Yang-Baxter equations

DOI10.1016/0167-2789(85)90058-2zbMath0584.35008OpenAlexW2094234100WikidataQ56950864 ScholiaQ56950864MaRDI QIDQ1070420

Craig A. Tracy

Publication date: 1985

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(85)90058-2

zbMATH Keywords

elliptic curvesvertex modelspolynomial equations

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Elliptic curves (14H52) Theta functions and abelian varieties (14K25) Qualitative properties of solutions to partial differential equations (35B99)

Related Items (11)

A simple construction of elliptic \(R\)-matrices ⋮ The emerging role of number theory in exactly solvable models in lattice statistical mechanics ⋮ Elliptic K-matrix associated with Belavin's symmetric R-matrix ⋮ The dynamical Yang–Baxter relation and the minimal representation of the elliptic quantum group ⋮ Deformed Virasoro algebras from elliptic quantum algebras ⋮ Elliptic R-matrices and Feigin and Odesskii's elliptic algebras ⋮ Simple construction of the elliptic boundary \(K\)-matrix ⋮ Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings ⋮ Integrable mappings and soliton equations. II ⋮ The quantum determinant of the elliptic algebra $ {\mathcal{A}_{q, p}(\mathfrak{\widehat{gl}}_N)}$ ⋮ Segre threefold and \(N=3\) reflection equation

Cites Work

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• Dynamical symmetry of integrable quantum systems
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Partition function of the eight-vertex lattice model
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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