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)

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)

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 study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free fieldâ€¦ (More)

Soliton equations are known as non-linear partial differential equations with infinite dimensional symmetry. For example, KP (Kadomtzev Petviashvili) hierarchy has GLâˆž-symmetry and KdV (Korteweg-deâ€¦ (More)

A vertex algebra V , used to construct a rational conformal field theory, must satisfy at least the following three conditions: (a) V has only finitely many irreducible representations {Mj}jâˆˆJ , (b)â€¦ (More)

We describe a conjectural classification of Poisson vertex algebras of CFT type and of Poisson vertex algebras in one differential variable (= scalar Hamiltonian operators). Transformation Groups 15â€¦ (More)

In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sum.

We study the quantum Hamiltonian reduction for affine superalge-bras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted onesâ€¦ (More)

In this note we calculate the fusion coefficients for minimal series representations of the N=2 superconformal algebra by using a modified Verlindeâ€™s formula, and obtain associative and commutativeâ€¦ (More)