Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs

Abstract

We present formulas for the Clebsch-Gordan coefficients and the Racah coefficients for the root of unity representations ($N$-dimensional representations with $q^{2N}=1$) of $U_q(sl(2))$. We discuss colored vertex models and colored IRF (Interaction Round a Face) models from the color representations of $U_q(sl(2))$. We construct invariants of trivalent colored oriented framed graphs from color representations of $U_q(sl(2))$.

39 pages, January 1992

Cited by in corpus (18)

• On the solutions to the multi-parametric Yang-Baxter equations
• Composition of Kinetic Momenta: The U_q(sl(2)) case
• Two elliptic height models with factorized domain wall partition functions
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Quantum Relatives of Alexander Polynomial
• Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
• Dual wavefunction of the Felderhof model
• Multivariable Invariants of Colored Links Generalizing the Alexander Polynomial
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity: cyclic representations
• Free fermions in classical and quantum integrable models
• Dual wavefunction of the symplectic ice
• Studies in Integrable Quantum Lattice Models and Classical Hierarchies
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• Scalar products of the elliptic Felderhof model and elliptic Cauchy formula
• The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity
• On the Moyal quantized BKP type hierarchies
• Elliptic free-fermion model with OS boundary and elliptic Pfaffians
• Seifert-Torres Type Formulas for the Alexander Polynomial from Quantum ${\mathfrak{sl}}_2$