Duke Mathematical Journal

Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials

B. Feigin, M. Jimbo, R. Kedem, S. Loktev, and T. Miwa

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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.

Article information

Duke Math. J., Volume 125, Number 3 (2004), 549-588.

First available in Project Euclid: 18 November 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65]


Feigin, B.; Jimbo, M.; Kedem, R.; Loktev, S.; Miwa, T. Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials. Duke Math. J. 125 (2004), no. 3, 549--588. doi:10.1215/S0012-7094-04-12533-3. https://projecteuclid.org/euclid.dmj/1100793679

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