TY - JOUR
T1 - Spaces of coinvariants and fusion product II. sl2 character formulas in terms of Kostka polynomials
AU - Feigin, B.
AU - Jimbo, M.
AU - Kedem, R.
AU - Loktev, S.
AU - Miwa, T.
PY - 2004/9/1
Y1 - 2004/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=4043154411&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2004.03.004
DO - 10.1016/j.jalgebra.2004.03.004
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AN - SCOPUS:4043154411
SN - 0021-8693
VL - 279
SP - 147
EP - 179
JO - Journal of Algebra
JF - Journal of Algebra
IS - 1
ER -