Systems of correlation functions, coinvariants, and the Verlinde Algebra

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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
Issue number1
StatePublished - Mar 2012
Externally publishedYes


FundersFunder number
Leading Scientific Schools3472.2008.2
EADS Foundation Wales
Russian Foundation for Basic Research07-02-00799, 09-01-00058


    • Zhu algebra
    • affine Lie algebra
    • vertex operator algebra


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