On modules over matrix quantum pseudo-differential operators

Abstract

We classify all the quasifinite highest-weight modules over the central extension of the Lie algebra of matrix quantum pseudo-differential operators, and obtain them in terms of representation theory of the Lie algebra gl(∞, Rm) of infinite matrices with only finitely many nonzero diagonals over the algebra Rm = ℂ[t]/(tm+1). We also classify the unitary ones.