Vertex operator algebras associated to type G affine Lie algebras

JOURNAL OF ALGEBRA

卷:337

Article

Axtell, Jonathan D.¹  Lee, Kyu-Hwan¹ 

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

关键词: Vertex operator algebras;    Affine Lie algebras;    Admissible levels;    Irreducible representations;    Singular vectors;   

DOI  :  10.1016/j.jalgebra.2011.04.028

来源: Elsevier

【 摘 要 】

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 G(2)((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 O. Applying the A(V)-theory, we prove that there are only finitely. many irreducible weak L(k,0)-modules from the category O and that such an L(k,0)-module is completely reducible. Our result supports the conjecture made by Adamovic and Milas (1995) [2]. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free