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

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

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

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s10688-012-0005-5

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title = "Systems of correlation functions, coinvariants, and the Verlinde Algebra",

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.",

keywords = "Zhu algebra, affine Lie algebra, vertex operator algebra",

author = "Feigin, \{E. B.\}",

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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doi = "10.1007/s10688-012-0005-5",

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AU - Feigin, E. B.

N1 - 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’s fund based on his 2004 Balzan prize in mathematics, and by EADS Foundation Chair in mathematics.

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N2 - 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.

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.

KW - Zhu algebra

KW - affine Lie algebra

KW - vertex operator algebra

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U2 - 10.1007/s10688-012-0005-5

DO - 10.1007/s10688-012-0005-5

M3 - مقالة

SN - 0016-2663

VL - 46

SP - 41

EP - 52

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

IS - 1

ER -

Systems of correlation functions, coinvariants, and the Verlinde Algebra

Abstract

Keywords

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