Quasifinite representations of the orthogonal Lie subralgebra of the Lie algebra of matrix differential operators on the circle

C. BOYALLIAN Y V. MEINARDI

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2010 vol. 51 p. 12 - 36

0022-2488

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 representations theory of the complex Lie algebra gl^[m]_\infty 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 B and D.gl^[m]_\infty 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 B and D.