  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.
