Solutions of the triangle equations withZ n×Zn-symmetry and matrix analogs of the Weierstrass zeta- and sigma-functions

Abstract

The matrix analogs of Weierstrass's zeta and sigma functions are introduced. It is proved that in the case ofZn×Zn-symmetry the classicalΤ-matrix coincides with the matrix zeta-function, whereas the quantumR-matrix is expressible as a ratio of matrix sigma-functions. The obtained formulas are considered to be the result of averaging over the period lattice.