QHWM of the orthogonal type Lie subalgebra of the Lie algebra of matrix differential operators on the circle

Abstract

In this paper we classify the irreducible quasifinite highest weight modules of the orthogonal Lie subalgebra of the Lie algebra of matrix differential operators on the circle. We also realize them 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 and the corresponding subalgebras of type B and D.