This preprint was accepted June, 1997.
ABSTRACT: For the $sl_2$ Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss decomposition for the $SL_2$ loop group. From the generating function a new explicit expression for the correlators is derived from which the determinant formulas for the norms of Bethe eigenfunctions due to Richardson and Gaudin are obtained.
[ Full text: ( .ps.gz) ]