Dualities and vertex operator algebras of affine type

2002/12/12 by Julius Borcea
Mathematics · #math.QA #math.RT

paper · pdf

published as Journal of Algebra vol. 258 nr. 2 (2002), 389-441 · 32 pages, no figures

arxiv created 2002/12/12 · arxiv updated 2009/11/30

Abstract

We notice that for any positive integer k, the set of (1,2)-specialized characters of level k standard A₁⁽¹⁾-modules is the same as the set of rescaled graded dimensions of the subspaces of level 2k+1 standard A₂⁽²⁾-modules that are vacuum spaces for the action of the principal Heisenberg subalgebra of A₂⁽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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