Rationality and fusion rules of exceptional -algebras

  • Tomoyuki Arakawa

    Kyoto University, Japan
  • Jethro van Ekeren

    Universidade Federal Fluminense, Niterói, Brazil
Rationality and fusion rules of exceptional  $\mathcal {W}$-algebras cover
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Abstract

First, we prove the Kac–Wakimoto conjecture on modular invariance of characters of exceptional affine -algebras. In fact more generally we prove modular invariance of characters of all lisse -algebras obtained through Hamiltonian reduction of admissible affine vertex algebras. Second, we prove the rationality of a large subclass of these -algebras, which includes all exceptional -algebras of type and lisse subregular -algebras in simply laced types. Third, for the latter cases we compute -matrices and fusion rules. Our results provide the first examples of rational -algebras associated with nonprincipal distinguished nilpotent elements, and the corresponding fusion rules are rather mysterious.

Cite this article

Tomoyuki Arakawa, Jethro van Ekeren, Rationality and fusion rules of exceptional -algebras. J. Eur. Math. Soc. 25 (2023), no. 7, pp. 2763–2813

DOI 10.4171/JEMS/1250