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Cyclotomic Schur Algebras and Blocks of Cyclic Defect

Published online by Cambridge University Press:  20 November 2018

Steffen König
Steffen König*
Affiliation:
Fakultät für Mathematik Universität Bielefeld Postfach 10 01 31 D–33501 Bielefeld Germany, e-mail: [email protected]
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Abstract

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An explicit classification is given of blocks of cyclic defect of cyclotomic Schur algebras and of cyclotomic Hecke algebras, over discrete valuation rings.

Keywords

20G0520C2016G3017B3757M25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 79 - 86
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Alperin, J. L., Local representation theory. Cambridge University Press, 1986.Google Scholar
[2] Ariki, S., On the decomposition numbers of the Hecke algebra of (m, 1, n). J. Math. Kyoto Univ. 36 (1996), 789–808.Google Scholar
[3] Ariki, S. and Koike, K., A Hecke algebra of Σn and construction of its irreducible representations. Adv. in Math. 106 (1994), 216–243.Google Scholar
[4] Broué, M. and Malle, G., Zyklotomische Heckealgebren. Astérisque 212 (1993), 119–189.Google Scholar
[5] Cline, E., Parshall, B. and Scott, L., Finite dimensional algebras and highest weight categories. J. Reine Angew. Math. 391 (1988), 85–99.Google Scholar
[6] Cline, E., Parshall, B. and Scott, L., Integral and graded quasi-hereditary algebras. I. J. Algebra 131 (1990), 126–160.Google Scholar
[7] Dipper, R. and James, G., The q–Schur algebra. Proc. LondonMath. Soc. 59 (1989), 23–50.Google Scholar
[8] Dipper, R., James, G. and Mathas, A., Cyclotomic q-Schur algebras. Math. Z. 229 (1998), 385–416.Google Scholar
[9] Erdmann, K., Schur algebras of finite type.Quart. J. Math.Oxford Ser. (2) 44 (1993), 17–41.Google Scholar
[10] Graham, J. J. and Lehrer, G. I., Cellular algebras. Invent. Math. 123 (1996), 1–34.Google Scholar
[11] König, S. and Xi, C. C., On the structure of cellular algebras. Algebras and modules II, Geiranger, 1996, 365– 386, CMS Conf. Proc. 24(1998), Amer. Math. Soc.Google Scholar
[12] König, S. and Xi, C. C., Cellular algebras: inflations and Morita equivalences. J. London Math. Soc., to appear.Google Scholar
[13] Parshall, B. and Scott, L. L., Derived categories, quasi–hereditary algebras and algebraic groups. Proc. of the Ottawa-MoosoneeWorkshop in Algebra 1987,Math. Lect. Note Series, Carleton University and Université d’Ottawa, 1988.Google Scholar
[14] Roggenkamp, K. W., Blocks of cyclic defect and Green-orders. Comm. Algebra 20 (1992), 1715–1734.Google Scholar
[15] Xi, C. C., The structure of Schur algebras Sk(n, p) for n ≥ p. Canad. J. Math. 44 (1992), 665–672.Google Scholar