Quasi-finite highest weight modules over W N ∞

Abstract

n this paper, we classify the irreducible quasi-finite highest weight modules of the Lie subalgebras WN ∞,p of the Lie algebra of matrix differential operators on the circle. We also realize the WN ∞-modules in terms of the representation theory of the complex Lie algebra g[m] ∞ of infinite matrices with a finite number of nonzero diagonals with entries in the algebra of truncated polynomials.