English

A proof of the fusion rules theorem

Quantum Algebra 2023-02-22 v3 Complex Variables

Abstract

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the same data. This provides a new proof and alternative version of Frenkel and Zhu's fusion rules theorem in terms of the dimension of certain bimodules over Zhu's algebra, without the assumption of rationality.

Keywords

Cite

@article{arxiv.2009.14622,
  title  = {A proof of the fusion rules theorem},
  author = {Jianqi Liu},
  journal= {arXiv preprint arXiv:2009.14622},
  year   = {2023}
}