HIROTA EQUATIONS FOR FUNDAMENTAL REPRESENTATIONS OF AN(1)

In a previous paper the m-principal fundamental representations of gl∞ were introduced. The Hirota equations associated with the fundamental representations were also derived. They turn out to be the same as the equations previously obtained by Date et al. and associated with the matrix realisation of gl∞ denoted by gl(m∞). It was shown that the J-reductions of gl(m∞) produce a complete set of realisations of an(1), though the fundamental representations of an(1) cannot simply be obtained by the J-reductions of the fundamental representations of gl(m∞). In the usual approach it would be necessary to obtain the fundamental representations of the twisted realisations of an(1) and then derive the Hirota equations for each such representation. However the Hirota equations for a complete non-redundant set of fundamental representations of an(1) can be obtained directly from the J-reductio n of the Hirota equations for the m-principal representations of gl∞. © 1990.