This article is cited in 1 paper

Systems of Correlation Functions, Coinvariants, and the Verlinde Algebra

E. B. Feigin<sup>ab

a</sup> P. N. Lebedev Physical Institute, Russian Academy of Sciences
^b Independent University of Moscow

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

Keywords: affine Lie algebra, vertex operator algebra, Zhu algebra.

UDC: 512.818.4

Received: 29.03.2010

DOI: 10.4213/faa3059

 English version: DOI: 10.1007/s10688-012-0005-5

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