As is well-known, nonunitary RCFTs are distinguished from unitary ones in a
number of ways, two of which are that the vacuum 0 doesn't have minimal
conformal weight, and that the vacuum column of the modular S matrix isn't
positive. However there is another primary field, call it o, which has minimal
weight and has positive S column. We find that often there is a precise and
useful relationship, which we call the Galois shuffle, between primary o and
the vacuum; among other things this can explain why (like the vacuum) its
multiplicity in the full RCFT should be 1. As examples we consider the minimal
WSU(N) models. We conclude with some comments on fractional level admissible
representations of affine algebras. As an immediate consequence of our
analysis, we get the classification of an infinite family of nonunitary WSU(3)
minimal models in the bulk.Comment: 24 page