Classification of irreducible modules of certain subalgebras of free boson vertex algebra

Let M(1) be the vertex algebra for a single free boson. We classify irreducible modules of certain vertex subalgebras of M(1) generated by two generators. These subalgebras correspond to the W(2, 2p-1)--algebras with central charge $1- 6 \frac{(p - 1) ^{2}}{p}$ where p is a positive integer, $p \ge 2$. We also determine the associated Zhu's algebras.Comment: 21 pages, Late

A construction of some ideals in affine vertex algebras

Let N_{k} (\g) be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or $C_{\ell} ^{(1)}$. We construct a family of ideals J_{m,n} (\g) in N_{k} (\g), and a family V_{m,n} (\g) of quotient VOAs. These families include VOAs associated to the integrable representations, and VOAs associated to admissible representations at half-integer levels investigated in q-alg/9502015. We also explicitly identify the Zhu's algebras A(V_{m,n} (\g)) and find a connection between these Zhu's algebras and Weyl algebras.Comment: 10 pages, Latex, minor change

A realization of certain modules for the N=4N=4 superconformal algebra and the affine Lie algebra A2(1)A_2 ^{(1)}

We shall first present an explicit realization of the simple $N=4$ superconformal vertex algebra $L_{c} ^{N=4}$ with central charge $c=-9$. This vertex superalgebra is realized inside of the $b c \beta \gamma$ system and contains a subalgebra isomorphic to the simple affine vertex algebra $L_{A_1} (- \tfrac{3}{2} \Lambda_0)$. Then we construct a functor from the category of $L_{c} ^{N=4}$--modules with $c=-9$ to the category of modules for the admissible affine vertex algebra $L_{A_{2} } (-\tfrac{3}{2} \Lambda_0)$. By using this construction we construct a family of weight and logarithmic modules for $L_{c} ^{N=4}$ and $L_{A_{2} } (-\tfrac{3}{2} \Lambda_0)$. We also show that a coset subalgebra of $L_{A_{2} } (-\tfrac{3}{2} \Lambda_0)$ is an logarithmic extension of the $W(2,3)$--algebra with $c=-10$. We discuss some generalizations of our construction based on the extension of affine vertex algebra $L_{A_1} (k \Lambda_0)$ such that $k+2 = 1/p$ and $p$ is a positive integer.Comment: 27 page

On W-algebra extensions of (2,p) minimal models: p > 3

This is a continuation of arXiv:0908.4053, where, among other things, we classified irreducible representations of the triplet vertex algebra W_{2,3}. In this part we extend the classification to W_{2,p}, for all odd p>3. We also determine the structure of the center of the Zhu algebra A(W_{2,p}) which implies the existence of a family of logarithmic modules having L(0)-nilpotent ranks 2 and 3. A logarithmic version of Macdonald-Morris constant term identity plays a key role in the paper.Comment: 19 page