Quasi-rational fusion products

TL;DR

This paper extends the concept of fusion to arbitrary lowest weight representations of W-algebras, providing explicit algorithms and exploring the properties of quasirational representations, which may relate to finite quantum dimensions.

Contribution

It introduces a generalized fusion framework for non-rational W-algebra representations and defines a stable quasirational category with potential links to quantum dimensions.

Findings

Fusion defined for arbitrary lowest weight representations

Explicit algorithms for fusion provided

Quasirational representations form a stable category

Abstract

Fusion is defined for arbitrary lowest weight representations of $W$-algebras, without assuming rationality. Explicit algorithms are given. A category of quasirational representations is defined and shown to be stable under fusion. Conjecturally, it may coincide with the category of representations of finite quantum dimensions.