Spaces of coinvariants and fusion product II. Affine sl_2 character formulas in terms of Kostka polynomials

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dc.creatorFeigin, B.
dc.creatorJimbo, M.
dc.creatorKedem, R.
dc.creatorLoktev, S.
dc.creatorMiwa, T.
dc.date2002-08-21
dc.date2002-10-08
dc.date.accessioned2026-07-07T09:21:17Z
dc.date.available2026-07-07T09:21:17Z
dc.descriptionIn this paper, we continue our study of the Hilbert polynomials of coinvariants begun in our previous work math.QA/0205324 (paper I). We describe the sl_n-fusion products for symmetric tensor representations following the method of Feigin and Feigin, and show that their Hilbert polynomials are A_{n-1}-supernomials. We identify the fusion product of arbitrary irreducible sl_n-modules with the fusion product of their resctriction to sl_{n-1}. Then using the equivalence theorem from paper I and the results above for sl_3, we give a fermionic formula for the Hilbert polynomials of a class of affine sl_2-coinvariants in terms of the level-restricted Kostka polynomials. The coinvariants under consideration are a generalization of the coinvariants studied in [FKLMM]. Our formula differs from the fermionic formula established in [FKLMM] and implies the alternating sum formula conjectured in [FL] for this case.
dc.description30 pages
dc.identifierhttps://arxiv.org/abs/math/0208156
dc.identifierhttp://arxiv.org/abs/math/0208156
dc.identifierJ. Algebra 279 (2004), no. 1, 147--179.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154967
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject17B67
dc.titleSpaces of coinvariants and fusion product II. Affine sl_2 character formulas in terms of Kostka polynomials
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