We find all the diagonal K-matrices for the R-matrix associated with the minimal representation of the exceptional affine algebra G (1) 2. The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe ansatz. We find many similarities with the case of the Izergin-Korepin R-matrix associated with the affine algebra A (2) 2 .

We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of generators of the RE algebra related to a finite rank even Hecke symmetry are derived.

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite dimensional C∗-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algortihms.