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.

N1 - Funding Information:
This work is partially supported by the Grant-in-Aid for Scientific Research (B2) no. 12440039, no. 14340040 and (A1) no. 13304010, Japan Society for the Promotion of Science. B. Feigin is partially supported by grants RFBR 02-01-01015 and INTAS-00-00055. The work of S. Loktev is partially supported by the grant RFBR-01-01-00546. The last stage of this work was carried out while the authors were visiting Mathematical Sciences Research Institute, Berkeley, March 2002.

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

UR - http://www.scopus.com/inward/citedby.url?scp=4043154411&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2004.03.004

DO - 10.1016/j.jalgebra.2004.03.004

M3 - Article

AN - SCOPUS:4043154411

VL - 279

SP - 147

EP - 179

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -