2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153826A 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.8 pages, latex, to appear in the Proceedings of Nonlinear Physics, ItalyExactly Solvable and Integrable Systemstext