The $n$-component KP hierarchy and representation theory

Starting from free charged fermions we give equivalent definitions of the $n/$-component KP hierarchy, in terms of $tau/$-functions $tau_alpha/$ (where $alpha in M =/$ root lattice of $sl_n/$), in terms of $n times n/$ matrix valued wave functions $W_alpha(alphain M)/$, and in terms of pseudodifferential wave operators $P_alpha(alphain M)/$. These imply the deformation and the zero curvature equations. We show that the 2-component KP hierarchy contains the Davey-Stewartson system and the $ngeq3/$ component KP hierarchy continues the $n/$-wave interaction equations. This allows us to construct theis solutions.