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

Abstract

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.