Generalized parafermions of orthogonal type

Creutzig T, Kovalchuk V, Linshaw AR (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Journal of Algebra Elsevier

Book Volume: 593

Pages Range: 178-192

DOI: 10.1016/j.jalgebra.2021.11.014

Abstract

There is an embedding of affine vertex algebras V^k(gln)↪V^k(sln+1), and the coset C^k(n)=Com(V^k(gln),V^k(sln+1)) is a natural generalization of the parafermion algebra of sl2. It was called the algebra of generalized parafermions by the third author and was shown to arise as a one-parameter quotient of the universal two-parameter W∞-algebra of type W(2,3,…). In this paper, we consider an analogous structure of orthogonal type, namely D^k(n)=Com(V^k(so2n),V^k(so2n+1))^Z2. We realize this algebra as a one-parameter quotient of the two-parameter even spin W∞-algebra of type W(2,4,…), and we classify all coincidences between its simple quotient Dk(n) and the algebras Wℓ(so2m+1) and Wℓ(so2m)^Z2. As a corollary, we show that for the admissible levels k=−(2n−2)+[Formula presented](2n+2m−1) for soˆ2n the simple affine algebra Lk(so2n) embeds in Lk(so2n+1), and the coset is strongly rational. As a consequence, the category of ordinary modules of Lk(so2n+1) at such a level is a braided fusion category.

Authors with CRIS profile

Thomas Creutzig

Involved external institutions

University of Alberta

Canada (CA) University of Denver

United States (USA) (US)

How to cite

APA:

Creutzig, T., Kovalchuk, V., & Linshaw, A.R. (2022). Generalized parafermions of orthogonal type. Journal of Algebra, 593, 178-192. https://doi.org/10.1016/j.jalgebra.2021.11.014

MLA:

Creutzig, Thomas, Vladimir Kovalchuk, and Andrew R. Linshaw. "Generalized parafermions of orthogonal type." Journal of Algebra 593 (2022): 178-192.

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