Vertex operator algebras associated to certain admissible modules for affine Lie algebras of type A
Abstract
Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that vertex operator algebra which are in category $\cal{O}$ as modules for the associated affine Lie algebra. We classify irreducible objects in that category and prove semisimplicity of that category.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2007
- DOI:
- 10.48550/arXiv.0707.4129
- arXiv:
- arXiv:0707.4129
- Bibcode:
- 2007arXiv0707.4129P
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory;
- 17B69
- E-Print:
- 21 pages, LaTeX