Classification of Non-Affine Non-Hecke Dynamical R-Matrices

Details Classification of Non-Affine Non-Hecke Dynamical R-Matrices Classification of Non-Affine Non-Hecke Dynamical R-Matrices

2012-04-12

arxiv.org/abs/1204.2746v2

Physics

Mathematical Physics

Scientific paper

A complete classification of non-affine dynamical quantum R-matrices obeying the Gl_n(C)-Gervais-Neveu-Felder equation is given without assuming either Hecke or weak Hecke conditions. More general dynamical dependences are observed. It is shown that any solution is built upon elementary blocks, which individually satisfy the weak Hecke condition. Each solution is in particular characterized by an arbitrary partition {I(i),i\in N^*_n} of the set of indices N^*_n into classes, I(i) being the class of the index i, and an arbitrary family of signs (e_I)_I\in{I(i),i\in N^*_n} on this partition. The weak Hecke-type R-matrices exhibit the analytical behaviour R_ij,ji=f(e_I(i)L_I(i)-e_I(j)L_I(j)), where f is a particular trigonometric or rational function, where L_I(i)=\sum_j\in I(i)l_j, with (l_i)_i\in N^*_n denoting the family of dynamical coordinates.

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