Infinitely dimensional Lax structure for one-dimensional Hubbard model

We report a two-parametric irreducible infinitely dimensional representation of the Lax integrability condition for the fermi Hubbard chain. Besides being of fundamental interest, hinting on possible novel quantum symmetry of the model, our construction allows for an explicit representation of an exact steady state many-body density operator for non-equilibrium boundary-driven Hubbard chain with arbitrary (asymmetric) particle source/sink rates at the letf/right end of the chain and with arbitrary boundary values of chemical potentials.