Singular Vectors and Zhu’s Poisson Algebra of Parafermion Vertex Operator Algebras

Sheets and associated varieties of affine vertex algebras

“…for a homogeneous element a ∈ V, see [ALY14]. Let us note that the homomorphism η V is not an isomorphism in general.…”

Fusion rules for the orbifold vertex operator algebras $L_{\widehat{\frak{sl}_2}}(k,0)^{K}$

“…We now recall some results from [DLY09], [DJWY10], [ALY14], [JW19], and [JW20]. Let K 0 = K(sl 2 , k) be the commutant vertex oparator algbera of the Heisenberg vertex subalgebra of L(k, 0) generated by h(−1)1.…”

“…The irreducible K 0 -modules M i,j , for 0 ≤ i ≤ k, 0 ≤ j ≤ k − 1 were constructed in [DLY09], where K 0 = M 0,0 , and M i,j ∼ = M k−i,k−i+j . Theorem 8.2 in [ALY14] showed that the k(k+1) [ALY14] and rational [ALY19].…”

Logarithmic vertex algebras related to sp(4)

“…Over the last ten years, there has been extensive research on the parafermion vertex operator algebras linked to rational affine vertex operator algebras at positive integer levels, resulting in a comprehensive understanding of their structure [10,15,16]. However, for other levels, such as generic levels, their structure remains largely unknown.…”