Positivity and fusion of unitary modules for unitary vertex operator algebras (Research on algebraic combinatorics and representation theory of finite groups and vertex operator algebras)

Abstract

In this expository article, we describe several conjectures arising in the tensor product theory of unitary modules over unitary vertex operator algebras. These conjectures are motivated by the belief that the category of unitary modules over a suitably nice unitary VOA should be a unitary modular tensor category. Of particular interest is the 'positivity conjecture, ' which generalizes to non-rational VOAs and provides a candidate for tensor products of modules in this context. This article was prepared for submission to RIMS Kôkyûroku.