Quantum Gaudin model, spin chains, and universal characters

Abstract

In this paper, we will construct the connection between the quantum Gaudin model and the universal character hierarchy by a newly defined coupled master T-operator. The coupled master T-operator of the quantum Gaudin model satisfies the bilinear identity of the universal character hierarchy, which is an extension of the Kadomtsev–Petviashvili hierarchy. In addition, for the generalized quantum integrable spin chains with rational GL(N)-invariant R-matrices, we construct its coupled master T-operator, which represents a generating function for two-folds commuting quantum transfer matrices. The functional relations for the transfer matrices are equivalent to an infinite set of Hirota bilinear equations of the modified universal character hierarchy.