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

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

2010-11-20

arxiv.org/abs/1011.4591v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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