618 research outputs found
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 where p is a positive integer, . 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 or
. 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 superconformal algebra and the affine Lie algebra
We shall first present an explicit realization of the simple
superconformal vertex algebra with central charge . This
vertex superalgebra is realized inside of the system and
contains a subalgebra isomorphic to the simple affine vertex algebra . Then we construct a functor from the category of
--modules with to the category of modules for the
admissible affine vertex algebra . By
using this construction we construct a family of weight and logarithmic modules
for and . We also show
that a coset subalgebra of is an
logarithmic extension of the --algebra with . We discuss some
generalizations of our construction based on the extension of affine vertex
algebra such that and 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
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