Parafermion vertex operator algebras and 𝑊-algebras

Arakawa, Tomoyuki; Lam, Ching Hung; Yamada, Hiromichi

doi:10.1090/tran/7547

Parafermion vertex operator algebras and $W$-algebras
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by Tomoyuki Arakawa, Ching Hung Lam and Hiromichi Yamada PDF

Trans. Amer. Math. Soc. 371 (2019), 4277-4301 Request permission

Abstract:

We prove the conjectural isomorphism between the level $k$ $\widehat {\mathfrak {sl}}_2$-parafermion vertex operator algebra and the $(k+1,k+2)$-minimal series $W_k$-algebra for all $k \ge 2$. As a consequence, we obtain the conjectural isomorphism between the $(k+1,k+2)$-minimal series $W_k$-algebra and the coset vertex operator algebra $SU(k)_1\otimes SU(k)_1/SU(k)_2$.

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