  A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax
pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs
are nonlinearized into a hierarchy of commutative finite dimensional integrable
Hamiltonian systems and explicit integrals of motion may also be generated. The
corresponding binary nonlinearization procedure leads to a sort of involutive
solutions to every system in soliton hierarchy which are all of finite gap. An
illustrative example is given in the case of AKNS soliton hierarchy.
