In reference to Atiyah's book - "Geometry of Yang-Mills Fields" (1979).
In chapter 5, section 3, he describes how the monad construction for $Sp(n)$ potentials can be interpreted in terms of quaternionic data. One can rewrite the map
$A(z) : W \to V$, as defined in for the Monad(Horrocks) construction of algebraic vector bundles over complex-projective space, in terms of quaternionic variables, one gets the map
$$ A(x,y) = xC + yD.$$
I would like to understand from here, how one can get the specific form on C & D as seen in the page 2 of this paper (denoted by $b$,$a$ up to a transpose?).
This way one could describe the equivalence with the data of real and complex moment maps, after rewriting the istropic condition on $A$?