Generalized parafermions of orthogonal type
نویسندگان
چکیده
There is an embedding of affine vertex algebras $V^k(\mathfrak{gl}_n) \hookrightarrow V^k(\mathfrak{sl}_{n+1})$, and the coset $\mathcal{C}^k(n) = \text{Com}(V^k(\mathfrak{gl}_n), V^k(\mathfrak{sl}_{n+1}))$ a natural generalization parafermion algebra $\mathfrak{sl}_2$. It was called generalized parafermions by third author shown to arise as one-parameter quotient universal two-parameter $\mathcal{W}_{\infty}$-algebra type $\mathcal{W}(2,3,\dots)$. In this paper, we consider analogous structure orthogonal type, namely $\mathcal{D}^k(n) \text{Com}(V^k(\mathfrak{so}_{2n}), V^k(\mathfrak{so}_{2n+1}))^{\mathbb{Z}_2}$. We realize even spin $\mathcal{W}(2,4,\dots)$, classify all coincidences between its simple $\mathcal{D}_k(n)$ $\mathcal{W}_{\ell}(\mathfrak{so}_{2m+1})$ $\mathcal{W}_{\ell}(\mathfrak{so}_{2m})^{\mathbb{Z}_2}$. As corollary, show that for admissible levels $k -(2n-2) + \frac{1}{2} (2 n 2 m -1)$ $\widehat{\mathfrak{so}}_{2n}$ $L_k(\mathfrak{so}_{2n})$ embeds in $L_k(\mathfrak{so}_{2n+1})$, strongly rational. consequence, category ordinary modules $L_k(\mathfrak{so}_{2n+1})$ at such level braided fusion category.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2021.11.014