Geodesic
Systems of Correlation Functions, Coinvariants, and the Verlinde Algebra
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 49-64

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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.
Mots-clés : affine Lie algebra
Keywords: vertex operator algebra, Zhu algebra. 
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     author = {E. B. Feigin},
     title = {Systems of {Correlation} {Functions,} {Coinvariants,} and the {Verlinde} {Algebra}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a4/}
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E. B. Feigin. Systems of Correlation Functions, Coinvariants, and the Verlinde Algebra. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 49-64. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a4/