Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation

In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point \(\tau\) from the upper half-plane and an invertible \(n \times n\) matrix \(B\) with complex coefficients one can attach a solution of AYBE with values in \(Mat_{n \times n}(\CC) \otimes Mat_{n \times n}(\CC)\), depending holomorphically on \(\tau\) and \(B\). Moreover, we compute some of these solutions explicitly.