Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper of Nimmo (2006 J. Phys. A: Math. Gen. 39 5053-65) it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper, we discuss these solutions from a different perspective and show that the solutions are quasi-Pluecker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pluecker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared