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 ττ from the upper half-plane and an invertible (n×n)(n×n) matrix BB with complex coefficients, one can attach a solution of AYBE with values in Matn×n(C)⊗Matn×n(C), depending holomorphically on ττ and BB. Moreover, we compute some of these solutions explicitly.