  Quantum invariants of the orbit dependent pairing problem are identified in
the limit where the orbits become degenerate. These quantum invariants are
simultaneously diagonalized with the help of the Bethe ansatz method and a
symmetry in their spectra relating the eigenvalues corresponding to different
number of pairs is discussed. These quantum invariants are analogous to the
well known rational Gaudin magnet Hamiltonians which play the same role in the
reduced pairing case (i.e., orbit independent pairing with non degenerate
energy levels). It is pointed out that although the reduced pairing and the
degenerate cases are opposite of each other, the Bethe ansatz diagonalization
of the invariant operators in both cases are based on the same algebraic
structure described by the rational Gaudin algebra.
