Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle
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We give a complete description of the quasifinite highest weight modules over the central extension of the Lie algebra of M × M-matrix differential operators on the circle and obtain them in terms of representation theory of the Lie algebra ĝl(∞,Rm) of infinite matrices with only finitely many nonzero diagonals over the algebra Rm = 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 WM1 + ∞, c, where c is a positive integer. © 1998 American Institute of Physics.
author list (cited authors)
Boyallian, C., Kac, V. G., Liberati, J. I., & Yan, C. H.