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1 December 2004 Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials
B. Feigin, M. Jimbo, R. Kedem, S. Loktev, T. Miwa
Duke Math. J. 125(3): 549-588 (1 December 2004). DOI: 10.1215/S0012-7094-04-12533-3

Abstract

The fusion rule gives the dimensions of spaces of conformal blocks in Wess-Zumino-Witten (WZW) theory. We prove a dimension formula similar to the fusion rule for spaces of coinvariants of affine Lie algebras $\widehat{\mathfrak{g}}$. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weight $\widehat{\mathfrak{g}}$-modules and tensor products of finite-dimensional evaluation representations of $\mathfrak{g}\otimes \mathbb{C}[t]$.

In the $\widehat{\mathfrak{sl}}$2-case we prove that their associated graded spaces are isomorphic to the spaces of coinvariants of fusion products and that their Hilbert polynomials are the level-restricted Kostka polynomials.

Citation

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B. Feigin. M. Jimbo. R. Kedem. S. Loktev. T. Miwa. "Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials." Duke Math. J. 125 (3) 549 - 588, 1 December 2004. https://doi.org/10.1215/S0012-7094-04-12533-3

Information

Published: 1 December 2004
First available in Project Euclid: 18 November 2004

zbMATH: 1129.17304
MathSciNet: MR2166753
Digital Object Identifier: 10.1215/S0012-7094-04-12533-3

Subjects:
Primary: 17B65

Rights: Copyright © 2004 Duke University Press

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Vol.125 • No. 3 • 1 December 2004
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