  Using 4D Chern-Simons (CS) theory with gauge symmetry $G$ having minuscule
coweights, we develop a suitable operator basis to deal with the explicit
calculation of the Lax operator of integrable spin chain satisfying the RLL
equation. Using this basis, we derive the oscillator realisations of the full
list of the minuscule L-operators which are classified by the gauge symmetries
A$_{N}$, B$_{N}$, C$_{N}$, D$_{N}$, E$_{6}$, E$_{7}$. We also complete missing
results regarding the non simply laced $SO_{2N+1}$ and $SP_{2N}$ gauge
symmetries and comment on their intrinsic features. Moreover, we investigate
the properties of links reported in Yangian spin chain studies between the
(A-,D-) Lax operators and the (C-,B-) homologue. We show that these links are
due to discrete outer-automorphism symmetries that are explicitly worked out.
