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 $$\widehat{{\text{gl}}}$$ (∞, R m ) of infinite matrices with only finitely many nonzero diagonals over the algebra R m = $$\mathbb{C}$$ [t]/(t m+1). We also classify the unitary ones.
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