Universal R-matrix as integral operator

Abstract

We derive the integral operator form for the general rational solution of the Yang-Baxter equation with $s\ell (2|1)$ symmetry. Considering the defining relations for the kernel of the R-operator as a system of second order differential equations we observe remarkable reduction to a system of simple first order equations. The obtained kernel of R-operator has a very simple structure. To illustrate all this in the simplest situation we treat also the $s\ell (2)$ case.

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