\(gl_ q(n)\) and quantum monodromy (Q1194357)

An important step in the quantized sine-Gordon field theory is to search for a solution \(R\) of the quantum Yang-Baxter equation such that \(R T_ 1 T_ 2= T_ 2 T_ 1 R\), where \(T\) is the lattice transfer or monodromy matrix. The author considers the case when \(T = \exp \Phi\) in order to put into relief the monodromy interpretation; here \(\Phi = X^ i\ell_ i\). The problem of finding \(R\) can be solved if some algebraic relations on the \(X^ i\)'s are imposed; the analysis of such relations leads to the definition of a Hopf algebra \(gl_ q(n)\) [see also \textit{N. Reshetikhin}, Lett. Math. Phys. 20, 331-335 (1990; Zbl 0719.17006)].