Universal \(R\)-matrices for the quantum group \(U_ q(sl(N+1,\mathbb{C}))\): The root of unity case (Q1917005)

The author gives an explicit formula of a universal \(R\)-matrix for a quotient of the quantum group \(U_q(sl (n+1,\mathbb{C}))\) if \(q\) is a primitive \(r\)-th root of unity, \(r\neq 1,2,4\). The construction of the \(R\)-matrix is based on a pairing \(U^+\times U^-\to\mathbb{C}\), where \(U^+\) and \(U^-\) are Hopf subalgebras of \(U_q(sl (n+1,\mathbb{C}))\), and the pairing is compatible with its Hopf structures. To compensate the degeneration of the pairing in the case of \(q\) being a root of unity, it is necessary to pass to a quotient of the quantum group \(U_q(sl (n+1,\mathbb{C}))\).