Vertex operator algebras associated to admissible representations of $\hat{sl}_2$

Details Vertex operator algebras associated to admissible representations of $\hat{sl}_2$ Vertex operator algebras associated to admissible representations of $\hat{sl}_2$

1995-09-25

arxiv.org/abs/q-alg/9509026v1

Mathematics

Quantum Algebra

Latex 42 pages

Scientific paper

The admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebra. If $l$ is rational such that $l+2={p\over q}$ for some coprime positive integers $p\ge 2$ and $q$, Kac and Wakimoto found finitely many distinguished irreducible representations for $\hat{sl}_2$, called admissible representations. In this paper we prove that the vertex operator algebra $L(l,0)$ associated to irreducible highest weight representation of $l$ is not rational if $l$ is not a positive integer. However if we change the Virasoro algebra in certain way, $L(l,0)$ becomes a rational vertex operator algebra whose irreducible representations are exactly those admissible representations. We show that the $q$-dimensions with respect to the new Virasoro algebra are modular functions. We aslo calculate the fusions rules.

Affiliated with

Also associated with

No associations

Rating

Vertex operator algebras associated to admissible representations of $\hat{sl}_2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Vertex operator algebras associated to admissible representations of $\hat{sl}_2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vertex operator algebras associated to admissible representations of $\hat{sl}_2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-382681