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Dualities and vertex operator algebras of affine type

✍ Scribed by Julius Borcea

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 443 KB
Volume: 258
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00636-1

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✦ Synopsis

We notice that for any positive integer k, the set of (1, 2)-specialized characters of level k standard A

(1) 1 -modules is the same as the set of rescaled graded dimensions of the subspaces of level 2k + 1 standard A (2) 2 -modules that are vacuum spaces for the action of the principal Heisenberg subalgebra of A (2) 2 . We conjecture the existence of a semisimple category induced by the "equal level" representations of some algebraic structure which would naturally explain this duality-like property, and we study potential such structures in the context of generalized vertex operator algebras.

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