## Abstract

We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map {mapping} R(g) from GL(2,ℂ) × GL(1,ℂ) to End (V ⊗ V), where V is a two-dimensional vector space such that if g,h ε G then R_{12}(g)R_{13}(gh) R_{23}(h) = R_{23}(h) R_{13}(gh)R_{12}(g). Here R_{ij} denotes R applied to the i, j components of V ⊗ V ⊗ V. The image of this map consists of matrices whose nonzero coefficients a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2} are the Boltzmann weights for the non-field-free six-vertex model, constrained to satisfy a_{1}a_{2} + b_{1}b_{2} - c_{1}c_{2} = 0. This is the exact center of the disordered regime, and is contained within the free fermionic eight-vertex models of Fan and Wu. As an application, we show that with boundary conditions corresponding to integer partitions λ, the six-vertex model is exactly solvable and equal to a Schur polynomial s_{λ} times a deformation of the Weyl denominator. This generalizes and gives a new proof of results of Tokuyama and Hamel and King.

Original language | English (US) |
---|---|

Pages (from-to) | 281-301 |

Number of pages | 21 |

Journal | Communications in Mathematical Physics |

Volume | 308 |

Issue number | 2 |

DOIs | |

State | Published - Dec 2011 |