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

摘要

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