QHWM of the orthogonal and symplectic types Lie subalgebras of the Lie algebra of the matrix quantum pseudo differential operators

Abstract

In this paper we classify the irreducible quasifinite highest weight modules over the orthogonaland syplectic types Lie subalgebras of the Lie algebra of the matrix quantum pseudodifferential operators. We also realize them in terms of the irreducible quasifinite highestweight modules of the Lie algebras of infinite matrices with finitely many nonzero diagonalsand its classical Lie subalgebras of types B, C and D.