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Rationality of NeveuSchwarz vertex operator superalgebras

Summary: Rationality of Neveu­Schwarz vertex operator
DraŸzen Adamovi'c
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)


Source: Adamovic, Drazen - Department of Mathematics, University of Zagreb


Collections: Mathematics