Odd supersymmetric Kronecker elliptic function and Yang-Baxter equations

TL;DR

This paper introduces an odd supersymmetric version of the Kronecker elliptic function, extending its properties and applications to construct supersymmetric elliptic R-matrices satisfying key Yang-Baxter equations.

Contribution

It presents the first odd supersymmetric extension of the Kronecker elliptic function and constructs related R-matrices satisfying classical and associative Yang-Baxter equations.

Findings

Introduces an odd supersymmetric Kronecker elliptic function.

Constructs supersymmetric elliptic R-matrices.

Satisfies genus one Fay identity and supersymmetric heat equation.

Abstract

We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct an odd supersymmetric extensions of the elliptic $R$-matrices, which satisfy the classical and the associative Yang-Baxter equations.