R-matrices for highest weight representations of sl_q(2,C) at roots of unity

TL;DR

This paper derives a general formula for R-matrices of highest weight representations of sl_q(2,C), applicable for both generic q and roots of unity, extending previous specific cases.

Contribution

It generalizes existing formulas for R-matrices to all highest weight representations of sl_q(2,C), including at roots of unity, broadening the understanding of quantum group representations.

Findings

Provides a unified formula for R-matrices at roots of unity and generic q.

Extends previous work by G. Gomez and G. Sierra to all highest weight representations.

Enhances the mathematical framework for quantum group applications.

Abstract

The general formula for R-matrices of slq(2,C) for the highest weight repre- sentations both for general q and for q being a root of unity by generalizing G.Gomez's and G.Sierra's one for semiperiodic representations of slq(2,C) at roots of unity is presented.