Next, these are used to define the Lax matrix which is also a g valued function on the phase space which in addition depends meromorphically on a spectral parameter λ λ , L ( λ λ ) = ∑ ∑ r = 1 N X ( r ) λ λ − − λ λ r + Ω Ω , and Ω Ω is a constant element in g , in the sense that it Poisson commutes (has vanishing Poisson bracket) with all functions.