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Presenting cyclotomic q-Schur algebras

Published online by Cambridge University Press:  11 January 2016

Kentaro Wada*
Affiliation:
Graduate School of Mathematics Nagoya University, Nagoya 464-8602, Japan, kentaro-wada@math.nagoya-u.ac.jp
*
Research Institute for Mathematical Sciences Kyoto University, Kyoto 606-8502, Japan, wada@kurims.kyoto-u.ac.jp
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Abstract

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We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

[AK] Ariki, S. and Koike, K., A Hecke algebra of (Z/rZ) and construction of its irreducible representations, Adv. Math. 106 (1994), 216243.Google Scholar
[DDPW] Deng, B., Du, J., Parshall, B., and Wang, J., Finite Dimensional Algebras and Quantum Groups, Math. Surveys Monogr. 150, Amer. Math. Soc, Providence, 2008.Google Scholar
[DJM] Dipper, R., James, G., and Mathas, A., Cyclotomic q-Schur algebras, Math. Z. 229 (1998), 385416.Google Scholar
[Do] Doty, S., Presenting generalized q-Schur algebras, Represent. Theory 7 (2003), 196213.Google Scholar
[DG] Doty, S. and Giaquinto, A., Presenting Schur algebras, Int. Math. Res. Not. IMRN 36 (2002), 19071944.Google Scholar
[Du] Du, J., A note on quantized Weyl reciprocity at root of unity, Algebra Colloq. 2 (1995), 363372.Google Scholar
[DP] Du, J. and Parshall, B., Monomial bases for q-Schur algebras, Trans. Amer. Math. Soc. 355 (2003), 15931620.Google Scholar
[DR1] Du, J. and Rui, H., Based algebras and standard bases for quasi-hereditary alge bras, Trans. Amer. Math. Soc. 350 (1998), 32073235.Google Scholar
[DR2] Du, J. and Rui, H., Borel type subalgebras of the q-Schurm algebra, J. Algebra 213 (1999), 567595.Google Scholar
[GL] Graham, J. J. and Lehrer, G. I., Cellular algebras, Invent. Math. 123 (1996), 134.Google Scholar
[J] Jimbo, M., A q-analogue of U(gI(N + 1)), Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247252.Google Scholar
[KX] König, S. and Xi, C. C., On the structure of cellular algebras, Canad. Math. Soc. Conf. Proc. 24 (1998), 365386.Google Scholar
[M] Mathas, A., Iwahori-Hecke Algebras and Schur Algebras of the Symmetric Group, Univ. Lecture Ser. 15, Amer. Math. Soc, Providence, 1999.Google Scholar
[PW] Parshall, B. and Wang, J.-P., Quantum Linear Groups, Mem. Amer. Math. Soc. 89 (1991), no. 439.Google Scholar
[SakS] Sakamoto, M. and Shoji, T., Schur-Weyl reciprocity for Ariki-Koike algebras, J. Algebra 221 (1999), 293314.Google Scholar
[Saw] Sawada, N., On decomposition numbers of the cyclotomic q-Schur algebras, J. Algebra 311 (2007), 147177.Google Scholar
[SawS] Sawada, N. and Shoji, T., Modified Ariki-Koike algebras and cyclotomic q-Schur algebras, Math. Z. 249 (2005), 829867.Google Scholar
[S1] Shoji, T., A Frobenius formula for the characters of Ariki-Koike algebras, J. Algebra 226 (2000), 818856.Google Scholar
[S2] Shoji, T., personal communication, July 2007.Google Scholar
[SW] Shoji, T. and Wada, K., Cyclotomic q-Schur algebras associated to the Ariki-Koike algebra, Represent. Theory 14 (2010), 379416.Google Scholar