Dualities and vertex operator algebras of affine type

Details Dualities and vertex operator algebras of affine type Dualities and vertex operator algebras of affine type

2002-12-12

arxiv.org/abs/math/0212177v1

Journal of Algebra vol. 258 nr. 2 (2002), 389-441

Mathematics

Quantum Algebra

32 pages, no figures

Scientific paper

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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