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


  • 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 l(,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.

published proceedings

  • Journal of Mathematical Physics

author list (cited authors)

  • Boyallian, C., Kac, V. G., Liberati, J. I., & Yan, C. H.

citation count

  • 24

complete list of authors

  • Boyallian, Carina||Kac, Victor G||Liberati, José I||Yan, Catherine H

publication date

  • May 1998