Quasifinite representations of the Lie superalgebra of quantum pseudo differential operators

Abstract

In this paper we extend general results obtained by V. Kac and J. Liberati, in "Unitary quasifinite representations of $W_{\infty }$", (Letters Math. Phys., 53 (2000), 11-27), for quasifinite highest weight representations of $\mathbb{Z}$-graded Lie algebras to $1/2\mathbb{Z}$-graded Lie superalgebras, and we apply these to classify the irreducible quasifinite highest weight modules of the Lie superalgebra of quantum pseudo-differential operators.

23 pages