Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

Abstract

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.

34 pages, 2 figures

References in corpus (1)

• Non-Abelian Anyons and Topological Quantum Computation

Cited by in corpus (5)

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• Integrable Hamiltonians with $D(D_n)$ symmetry from the Fateev-Zamolodchikov model
• Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
• Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups
• Collective states of interacting $D(D_3)$ non-Abelian anyons