Classification of NonAffine NonHecke Dynamical RMatrices
Abstract
A complete classification of nonaffine dynamical quantum Rmatrices obeying the Gl_n({C})GervaisNeveuFelder equation is obtained 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),; iin\{1,dots,n}} of the set of indices {1,dots,n} into classes, {I}(i) being the class of the index i, and an arbitrary family of signs (∊_{I})_{{I}in{{I}(i), ; iin{1,dots,n}}} on this partition. The weak Hecketype Rmatrices exhibit the analytical behaviour R_{ij,ji}=f(∊_{{I}(i)}Λ_{{I}(i)}∊_{{I}(j)}Λ_{{I}(j)}), where f is a particular trigonometric or rational function, Λ_{{I}(i)}=sumlimits_{jin{I}(i)}λ_j, and (λ_i)_{iin{1,dots,n}} denotes the family of dynamical coordinates.
 Publication:

SIGMA
 Pub Date:
 September 2012
 DOI:
 10.3842/SIGMA.2012.064
 arXiv:
 arXiv:1204.2746
 Bibcode:
 2012SIGMA...8..064A
 Keywords:

 quantum integrable systems;
 dynamical YangBaxter equation;
 (weak) Hecke algebras;
 Mathematical Physics
 EPrint:
 SIGMA 8 (2012), 064, 45 pages