TY - JOUR
T1 - Spaces of coinvariants and fusion product, I
T2 - From equivalence theorem to kostka polynomials
AU - Feigin, B.
AU - Jimbo, M.
AU - Kedem, R.
AU - Loktev, S.
AU - Miwa, T.
PY - 2004/12/1
Y1 - 2004/12/1
N2 - 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 ̂g. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weights-modules and tensor products of finite-dimensional evaluation representations g ⊗ ℂ[t]. In the ̂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.
AB - 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 ̂g. An equivalence of filtered spaces is established between spaces of coinvariants of two objects: highest weights-modules and tensor products of finite-dimensional evaluation representations g ⊗ ℂ[t]. In the ̂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.
UR - https://www.scopus.com/pages/publications/11144279305
U2 - 10.1215/S0012-7094-04-12533-3
DO - 10.1215/S0012-7094-04-12533-3
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AN - SCOPUS:11144279305
SN - 0012-7094
VL - 125
SP - 549
EP - 588
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 3
ER -