Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle Academic Article uri icon

abstract

  • 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.

citation count

  • 23

publication date

  • May 1998