621 research outputs found
Vertex operator algebras associated to type B affine Lie algebras on admissible half-integer levels
Let L(n-l+1/2,0) be the vertex operator algebra associated to an affine Lie
algebra of type B_l^(1) at level n-l+1/2, for a positive integer n. We classify
irreducible L(n-l+1/2,0)-modules and show that every L(n-l+1/2,0)-module is
completely reducible. In the special case n=1, we study a category of weak
L(-l+3/2,0)-modules which are in the category as modules for the
associated affine Lie algebra. We classify irreducible objects in that category
and prove semisimplicity of that category.Comment: 40 pages, LaTeX; minor change
Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A
Let be the simple vertex operator algebra associated to an
affine Lie algebra of type with the lowest admissible
half-integer level , for even l. We study the category of weak
modules for that vertex operator algebra which are in category as
modules for the associated affine Lie algebra. We classify irreducible objects
in that category and prove semisimplicity of that category.Comment: 21 pages, LaTe
A note on representations of some affine vertex algebras of type D
In this note we construct a series of singular vectors in universal affine
vertex operator algebras associated to of levels ,
for . For , we study the representation theory of the
quotient vertex operator algebra modulo the ideal generated by that singular
vector. In the case , we show that the adjoint module is the unique
irreducible ordinary module for simple vertex operator algebra
. We also show that the maximal ideal in associated universal
affine vertex algebra is generated by three singular vectors.Comment: 9 page
Finite vs infinite decompositions in conformal embeddings
Building on work of the first and last author, we prove that an embedding of
simple affine vertex algebras , corresponding to an embedding of a maximal equal rank
reductive subalgebra into a simple Lie algebra ,
is conformal if and only if the corresponding central charges are equal. We
classify the equal rank conformal embeddings. Furthermore we describe, in
almost all cases, when decomposes finitely as a
-module.Comment: Latex file, 31 pages, minor corrections, to appear in Communications
in Mathematical Physic
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