Quasifinite Highest Weight Modules over Matrix Differential Operators on the circle.

CARINA BOYALLIAN, VICTOR KAC , JOSE LIBERATI AND KATHERIN H. YAN

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Año: 1998 vol. 39 p. 2910 - 2928

0022-2488

We give a complete description of the quasifinite highest weight modules over the central extension of the Lie algebra of matrix diferential operators on the circle and obtain them in terms of representation theory of the Lie algebra gl(\infty;R_m) of infinite matrices with only finitely many non-zero diagonals over the algebra R_m = C[t]^(tm+1). We also classify the unitary ones, and construct them in terms of charged free fermions. This construction provides a large (and conjecturally complete) family of irreducible modules over the associated vertex algebra W^M_{1+\infy;c},where c is a positive integer.