Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: $U_q(gl(m|n))$}

TL;DR

This paper constructs new solutions to the quantum Yang-Baxter equation for $U_q(gl(m|n))$ superalgebras, introducing R-matrices with additional continuous, non-additive parameters beyond the spectral parameter.

Contribution

It develops a method to generate R-matrices with extra non-additive parameters for quantum superalgebras, expanding the solution space of the Yang-Baxter equation.

Findings

New R-matrices with extra parameters constructed

Solutions depend on continuous non-additive parameters

Enhances understanding of quantum superalgebra representations

Abstract

The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum Yang-Baxter equation associated with the one-parameter family of irreps of $U_q(gl(m|n))$, thus obtaining R-matrices which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form.