Vertex Operator Algebras Associated to Type G Affine Lie Algebras

2010/11/15 by Jonathan D. Axtell, Axtell, Jonathan D., Kyu-Hwan Lee +1
Mathematics · #17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B69

paper · pdf · doi:10.48550/arxiv.1011.3473

30 pages

arxiv created 2010/11/15 · arxiv updated 2010/11/16

Abstract

In this paper, we study representations of the vertex operator algebra L(k,0) at one-third admissible levels k= -5/3, -4/3, -2/3 for the affine algebra of type G₂⁽¹⁾. We first determine singular vectors and then obtain a description of the associative algebra A(L(k,0)) using the singular vectors. We then prove that there are only finitely many irreducible A(L(k,0))-modules from the category \mathcal O. Applying the A(V)-theory, we prove that there are only finitely many irreducible weak L(k,0)-modules from the category \mathcal O and that such an L(k,0)-module is completely reducible. Our result supports the conjecture made by Adamović and Milas in \citeAM.

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