Representations of a symplectic type subalgebra of $W^N_{\infty }$W∞N

Abstract

In this paper we classify the irreducible quasifinite highest weight modules over the symplectic type Lie subalgebra of the Lie algebra of all regular differential operators on circle that kill constants. We also realize them in terms of the representations theory of the complex Lie algebra \documentclass[12pt]{minimal}\begin{document}$g\ell _\infty ^{[m]}$\end{document}gℓ∞[m] of infinite matrices with a finite number of non-zero diagonals with entries in the algebra of truncated polynomials and the corresponding subalgebras of type C.