Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. It turned out to be an adequate toolâ€¦ (More)

In our paper [KR] we began a systematic study of representations of the universal central extension DÌ‚ of the Lie algebra of differential operators on the circle. This study was continued in theâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1988

In this paper, we launch a program to describe and classify modular invariant representations of infinite-dimensional Lie algebras and superalgebras. We prove a character formula for a large class ofâ€¦ (More)

The Lie algebra DÌ‚, which is the unique non-trivial central extension of the Lie algebra D of differential operators on the circle [KP1], has appeared recently in various models of two-dimensionalâ€¦ (More)

The problem of representing an integer as a sum of squares of integers has had a long history. One of the first after antiquity was A. Girard who in 1632 conjectured that an odd prime p can beâ€¦ (More)

We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level 1 case. The analysis of this constructionâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1983

We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure ofâ€¦ (More)

Vertex operator algebras (VOA) were introduced in physics by Belavin, Polyakov and Zamolodchikov [BPZ] and in mathematics by Borcherds [B]. For a detailed exposition of the theory of VOAs see [FLM]â€¦ (More)

0.1. The remarkable link between the soliton theory and the group GL âˆž was discovered in the early 1980s by Sato [S] and developed, making use of the spinor formalism, by Date, Jimbo, Kashiwara andâ€¦ (More)