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We describe a parametrized Yang-Baxter equation with nonabelian parameter group. That is, we show that there is an injective map g → 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 ∈ 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.Baxter's method of solving lattice models in statistical mechanics is based on the star-triangle relation, which is the identitywhere R, S, T are endomorphisms of V ⊗ V for some vector space V . Here R ij is the endomorphism of V ⊗ V ⊗ V in which R is applied to the i-th and j-th copies of V 1

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Abstract. We provide an elementary and self-contained derivation of formulae for products and ratios of characteristic polynomials from classical groups using classical results due to Weyl and Littlewood.