Generating Function of Correlators in the sl2 Gaudin Model

An exponential generating function of correlators is calculated explicitly for the sl2 Gaudin model (degenerated quantum integrable XXX spin chain). The calculation relies on the Gauss decomposition for the SL(2) loop group. A new explicit expression for the correlators is derived from the generating function, from which the determinant formulas for the norms of Bethe eigenfunctions due to Richardson and Gaudin are obtained.