Sigma involutions associated with parafermion vertex operator algebra $K({\mathfrak{sl}}_2,k)$

Abstract

An irreducible module for the parafermion vertex operator algebra $K({\mathfrak{sl}}_2,k)$ is said to be of $\sigma$-type if an automorphism of the fusion algebra of $K({\mathfrak{sl}}_2,k)$ of order $k$ is trivial on it. For any integer $k\ge 3$, we show that there exists an automorphism of order $2$ of the subalgebra of the fusion algebra of $K({\mathfrak{sl}}_2,k{)}^{⟨\theta ⟩}$ spanned by the irreducible direct summands of $\sigma$-type irreducible $K({\mathfrak{sl}}_2,k)$-modules, where $\theta$ is an involution of $K({\mathfrak{sl}}_2,k)$. We discuss some examples of such an automorphism as well.

arXiv comment37 pages

References in corpus (6)

• Modular invariance of trace functions in orbifold theory
• C_2-cofiniteness of cyclic-orbifold models
• Tensor categories for vertex operator superalgebra extensions
• Fusion rules for ${\mathbb{Z}}_2$-orbifolds of affine and parafermion vertex operator algebras
• Uniqueness of VOA structure of 3C-algebra and 5A-algebra
• The VOAs generated by two Ising vectors e and f with <e,f>=1/2^8 or 3/2^9