Systems of correlation functions, coinvariants, and the Verlinde Algebra

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Abstract

We study the Gaberdiel-Goddard spaces of systems of correlation functions attached to affine Kac-Moody Lie algebras ĝ. We prove that these spaces are isomorphic to spaces of coinvariants with respect to certain subalgebras ofĝ. This allows us to describe the Gaberdiel-Goddard spaces as direct sums of tensor products of irreducible g-modules with multiplicities determined by the fusion coefficients. We thus reprove and generalize the Frenkel-Zhu theorem.

Original languageEnglish
Pages (from-to)41-52
Number of pages12
JournalFunctional Analysis and its Applications
Volume46
Issue number1
DOIs
Publication statusPublished - Mar 2012
Externally publishedYes

Keywords

  • affine Lie algebra
  • vertex operator algebra
  • Zhu algebra

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