ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 17 Liberati, José I., Massachusetts Institute of Technology, USA - UNC Quasifinite Highest Weight Modules over the Lie algebra of Matrix Differential Operators on the circle We describe 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 representations of the Lie algebra ĝl(∞, R_{m}), where R_{m} = ℂ[t]/(t^{m+1}). We 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_{1+∞,c}^{M}, where c ∈ ℕ. Reference: C. Boyallian, V. Kac, J. Liberati, C. Yan, “Quasifinite Highest Weight Modules over the Lie algebra of Matrix Differential Operators on the circle”, to appear in Jour. Math. Phys.