618 research outputs found

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

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    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 1βˆ’6(pβˆ’1)2p1- 6 \frac{(p - 1) ^{2}}{p} where p is a positive integer, pβ‰₯2p \ge 2. We also determine the associated Zhu's algebras.Comment: 21 pages, Late

    A construction of some ideals in affine vertex algebras

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    Let N_{k} (\g) be a vertex operator algebra (VOA) associated to the generalized Verma module for affine Lie algebra of type Aβ„“βˆ’1(1)A_{\ell -1} ^{(1)} or Cβ„“(1)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)}

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    We shall first present an explicit realization of the simple N=4N=4 superconformal vertex algebra LcN=4L_{c} ^{N=4} with central charge c=βˆ’9c=-9. This vertex superalgebra is realized inside of the bcΞ²Ξ³ b c \beta \gamma system and contains a subalgebra isomorphic to the simple affine vertex algebra LA1(βˆ’32Ξ›0)L_{A_1} (- \tfrac{3}{2} \Lambda_0). Then we construct a functor from the category of LcN=4L_{c} ^{N=4}--modules with c=βˆ’9c=-9 to the category of modules for the admissible affine vertex algebra LA2(βˆ’32Ξ›0)L_{A_{2} } (-\tfrac{3}{2} \Lambda_0). By using this construction we construct a family of weight and logarithmic modules for LcN=4L_{c} ^{N=4} and LA2(βˆ’32Ξ›0)L_{A_{2} } (-\tfrac{3}{2} \Lambda_0). We also show that a coset subalgebra of LA2(βˆ’32Ξ›0)L_{A_{2} } (-\tfrac{3}{2} \Lambda_0) is an logarithmic extension of the W(2,3)W(2,3)--algebra with c=βˆ’10c=-10. We discuss some generalizations of our construction based on the extension of affine vertex algebra LA1(kΞ›0)L_{A_1} (k \Lambda_0) such that k+2=1/pk+2 = 1/p and pp is a positive integer.Comment: 27 page

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

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    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
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