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We present an explicit construction of a family of steady state densitymatrices for an open integrable spin-1 chain with bilinear and biquadraticinteractions, also known as the Lai-Sutherland model, driven far fromequilibrium by means of two oppositely polarizing Markovian dissipationchannels localized at the boundary. The steady state solution exhibits n+1 folddegeneracy, for a chain of length n, due to existence of (strong) LiouvillianU(1) symmetry. The latter can be exploited to introduce a chemical potentialand define a grand canonical nonequilibrium steady state ensemble. The matrixproduct form of the solution entails an infinitely-dimensional representationof a non-trivial Lie algebra (semidirect product of sl_2 and a non-nilpotentradical) and hints to a novel Yang-Baxter integrability structure.

Exact steady state manifold of a boundary driven spin-1 Lai-Sutherland chain