Systems of correlation functions, coinvariants, and the Verlinde Algebra

E. B. Feigin

doi:10.1007/s10688-012-0005-5

Systems of correlation functions, coinvariants, and the Verlinde Algebra

E. B. Feigin

Higher School of Economics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English
Pages (from-to)	41-52
Number of pages	12
Journal	Functional Analysis and its Applications
Volume	46
Issue number	1
DOIs	https://doi.org/10.1007/s10688-012-0005-5
State	Published - Mar 2012
Externally published	Yes

Keywords

Zhu algebra
affine Lie algebra
vertex operator algebra

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10.1007/s10688-012-0005-5

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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.",

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note = "Funding Information: ∗This work was partially supported by the program for support of young candidates of sciences (grant no. MK-281.2009.1), by RFBR grants nos. 09-01-00058 and 07-02-00799, by the program “Leading Scientific Schools” (grant no. 3472.2008.2), by Pierre Deligne{\textquoteright}s fund based on his 2004 Balzan prize in mathematics, and by EADS Foundation Chair in mathematics.",

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AB - 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.

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Systems of correlation functions, coinvariants, and the Verlinde Algebra

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