Spaces of coinvariants and fusion product II. sl2 character formulas in terms of Kostka polynomials

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

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In this paper, we continue our study of the Hilbert polynomials of coinvariants begun in our previous work [B. Feigin et al., math.QA/0205324, 2002]. We describe the sln fusion products for symmetric tensor representations following the method of [B. Feigin, E. Feigin, math.QA/0201111, 2002], and show that their Hilbert polynomials are An-1-supernomials. We identify the fusion product of arbitrary irreducible sln -modules with the fusion product of their restriction to sln-1. Then using the equivalence theorem from [B. Feigin et al., math.QA/0205324, 2002] and the results above for sl3 we give a fermionic formula for the Hilbert polynomials of a class of sl2 coinvariants in terms of the level-restricted Kostka polynomials. The coinvariants under consideration are a generalization of the coinvariants studied in [B. Feigin et al., Transfom. Groups 6 (2001) 25-52; math.QA/0009198, 2000; math.QA/0012190, 2000]. Our formula differs from the fermionic formula established in [B. Feigin et al., Transfom. Groups 6 (2001) 25-52; QA/0012190 math.QA/0012190, 2000] and implies the alternating sum formula conjectured in [B. Feigin, S.; Loktev, QA/9812093 1998; Amer. Math. Sci. Transl. 194 (1999) 61-79] for this case.

Original languageEnglish (US)
Pages (from-to)147-179
Number of pages33
JournalJournal of Algebra
Issue number1
StatePublished - Sep 1 2004

ASJC Scopus subject areas

  • Algebra and Number Theory

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