Summary: Rationality of NeveuSchwarz vertex operator
superalgebras
DraŸzen Adamovi'c
Introduction
In this paper we study vertex operator superalgebras associated to the highest
weight modules for NeveuSchwarz algebra. The existence of the structure
of vertex operator superalgebra (SVOA) on these modules was first proved
in [KWn] and then later in [Li1]. From the point of view of representation
theory the most interesting are SVOAs L c associated to the minimal models
for NeveuSchwarz algebra (see Section 1). These SVOAs were investigated
by V. Kac and W. Wang in [KWn]. They conjectured the rationality of L c .
There is a close connection between representations of NeveuSchwarz
algebra and representations of affine Lie algebra A (1)
1 . By the results from
[GKO] and [KW 1] follow that every unitary representation for NeveuSchwarz
algebra appears in the tensor product of unitary representations for A (1)
1 with
the level two module F = L(2\Lambda 0 ) \Phi L(2\Lambda 1 ). This result has been greatly ex
tended in [KW 2] by replacing unitary representations with admissible repre
sentations of A (1)
