Quasifinite representations of the symplectic Lie subalgebra of W^n_{\infty}

C. BOYALLIAN; V. MEIANRDI

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 2011 vol. 52 p. 2910 - 2928

0022-2488

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 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.