English

Fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$

Quantum Algebra 2023-08-31 v1 Mathematical Physics math.MP Representation Theory

Abstract

We study the structure of fusion rules for the triplet WW-algebra Wp+,p\mathcal{W}_{p_+,p_-}. By using the vertex tensor category theory developed by Huang, Lepowsky and Zhang, we rederive certain non-semisimple fusion rules given by Gaberdiel-Runkel-Wood and Rasmussen. We further show that certain rank two and three indecomposable modules are self-dual.

Keywords

Cite

@article{arxiv.2308.15954,
  title  = {Fusion rules for the triplet $W$-algebra $\mathcal{W}_{p_+,p_-}$},
  author = {Hiromu Nakano},
  journal= {arXiv preprint arXiv:2308.15954},
  year   = {2023}
}

Comments

65 pages