Hostname: page-component-7b9c58cd5d-v2ckm Total loading time: 0 Render date: 2025-03-13T15:52:38.962Z Has data issue: false hasContentIssue false
  • English
  • Français

Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)

Published online by Cambridge University Press:  11 January 2016

Maria Chlouveraki
Maria Chlouveraki*
Affiliation:
University of Edinburgh, School of Mathematics, JCMB, King’s Buildings, Edinburgh, EH9 3JZ, UKmaria.chlouveraki@ed.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite series G(de, e, r), thus completing their calculation for all complex reflection groups.

Keywords

20C08
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 197 , March 2010 , pp. 175 - 212
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

[1] Ariki, S., Representation theory of a Hecke algebra of G(r,p,n), J. Algebra, 177 (1995), 164–185.Google Scholar
[2] Broué, M. and Kim, S., Familles de caractères des algèbres de Hecke cyclotomiques, Adv. Math., 172 (2002), 53–136.Google Scholar
[3] Broué, M., Malle, G., and Michel, J., Towards Spetses I, Trans. Groups, 4 (1999), 157–218.Google Scholar
[4] Broué, M., Malle, G., and Rouquier, R., Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math., 500 (1998), 127–190.Google Scholar
[5] Chlouveraki, M., Blocks and Families for Cyclotomic Hecke Algebras, Lecture Notes in Math., 1981, Springer, Berlin, 2009.Google Scholar
[6] Chlouveraki, M., Degree and valuation of the Schur elements of cyclotomic Hecke algebras, J. Algebra, 320 (2008), 3935–3949.Google Scholar
[7] Chlouveraki, M., Rouquier blocks of the cyclotomic Ariki-Koike algebras, Algebra Number Theory J., 2 (2008), 689–720.CrossRefGoogle Scholar
[8] Dade, E. C., Compounding Clifford’s theory, Ann. Math. (2), 91 (1970), 236–290.Google Scholar
[9] Geck, M., Beitr¨age zur Darstellungstheorie von Iwahori-Hecke-Algebren, RWTH Aachen, Habilitations-schrift, 1993.Google Scholar
[10] Geck, M. and Rouquier, R., Centers and simple modules for Iwahori-Hecke algebras, Progr. Math., 141 (1997), 251–272.Google Scholar
[11] Geck, M., Iancu, L., and Malle, G., Weights of Markov traces and generic degrees, Indag. Math. (N.S.), 11 (2000), 379–397.CrossRefGoogle Scholar
[12] Gyoja, A., Cells and modular representations of Hecke algebras, Osaka J. Math., 33 (1996), 307–341.Google Scholar
[13] Kim, S., Families of the characters of the cyclotomic Hecke algebras of G(de, e, r), J. Algebra, 289 (2005), 346–364.CrossRefGoogle Scholar
[14] Lusztig, G., Characters of Reductive Groups over a Finite Field, Ann. of Math. Stud. 107, Princeton Univ. Press, Princeton, 1984.Google Scholar
[15] Lusztig, G., Leading coefficients of character values of Hecke algebras, Proc. Symp. Pure Math., 47 (1987), 235–262.Google Scholar
[16] Malle, G., Degrés relatifs des algèbres cyclotomiques associées aux groupes de réflexions complexes de dimension deux, Progr. Math., 141 (1996), 311–332.Google Scholar
[17] Malle, G., On the rationality and fake degrees of characters of cyclotomic algebras, J. Math. Sci. Univ. Tokyo, 6 (1999), 647–677.Google Scholar
[18] Malle, G., Spetses, Doc. Math. J. DMV Extra Vol. ICM II (1998), 8796.Google Scholar
[19] Malle, G. and Rouquier, R., Familles de caractères de groupes de réflexions complexes, Represent. Theory, 7 (2003), 610–640.CrossRefGoogle Scholar
[20] Mathas, A., Matrix units and generic degrees for the Ariki-Koike algebras, J. Algebra, 281 (2004), 695–730.Google Scholar
[21] Rouquier, R., Familles et blocs d’algèbres de Hecke, C. R. Acad. Sci., 329 (1999), 1037–1042.Google Scholar