Abstract
| Conformal field theory is an essential tool of modern mathematical physics with
applications to string theory and to the critical behaviour of statistical
lattice models. The symmetries of a conformal field theory include all
angle-preserving transformations. In two dimensions, these transformations
generate the Virasoro algebra, a powerful symmetry that allows one to calculate
observable quantities analytically. The construction of one family of conformal
field theories from the affine Kac-Moody algebra sl(2) were proposed by Kent in
1986 as a means of generalising the coset construction to non-unitary Virasoro
minimal models, these are known as the Wess-Zumino-Witten models at admissible
levels. This talk aims to illustrate, with the example of the affine Kac-Moody
superalgebra osp(1|2) at admissible levels, how the representation theory of a
vertex operator superalgebra can be studied through a coset construction. The
method allows us to determine key aspects of the theory, including its module
characters, modular transformations and fusion rules. |