The number of simple modules of the Hecke algebras of type G(r, 1, n)

Mathematische Zeitschrift

Volumn 233, Issue 3, 2000, Pages 601-623

  Ariki, Susumu ^a   Mathas, Andrew ^b  

^a TOKYO UNIVERSITY OF MARINE SCIENCE AND TECHNOLOGY   (Japan)

^b UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347335     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002090050489     Document Type: Article

References (28)

1. S. Ariki, On the decomposition numbers of the Hecke algebra of G(m, 1, n), J. Math. Kyoto Univ.. 36 (1996), 789-808.
2. S. Ariki, On the classification of simple modules for cyclotomic Hecke algebras of type G(m, 1, n) and Kleshchev multipartitions, preprint, 1999.
3. n and construction of its irreducible representations, Adv. Math, 106 (1994), 216-243.
4. C.J. Bushnell, P. Kutzko, The Admissible Dual via Open Compact Groups, Annals of Math. Studies, 129 (1993), Princeton University Press.
5. N. Chriss, V. Ginzburg, Representation theory and complex geometry, Birkhäuser, Boston, 1997.
6. C. W. Curtis, I. Reiner, Methods of Representation Theory, Vols. I and II, John Wiley, New York, 1987.
7. R. Dipper, G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3), 52 (1986), 20-52.
8. R. Dipper. G. James, A. Mathas, Cyclotomic q-Schur algebras, Math. Zeit., 229 (1999), 385-416.
9. R. Dipper, A. Mathas, Morita equivalences of Ariki-Koike algebras, in preparation, (1999).
10. n-1 and Jantzen-Seitz problem for Ariki-Koike algebras, Adv. Math., to appear.
11. M. Geck, G. Hiß, Basic sets of Brauer characters for finite groups of Lie type, J. reine angew. Math., 418 (1991), 173-188.
12. M. Geck, G. Hiß. G. Malle, Towards a classification of the irreducible representations in non-describing characteristic of a finite group of Lie type, Math. Zeit., 221 (1996), 353-386.
13. J. J. Graham, G. I. Lehrer, Cellular algebras, Invent. Math., 123 (1996), 1-34.
14. T. Hayashi, q-analogues of Clifford and Weyl algebras, Comm. Math. Phys., 127 (1990), 129-144.
15. G. James, A. Mathas, The Jantzen sum formula for cyclotomic q-Schur algebras, Trans. A.M.S., to appear (accepted 1998).
16. q(sl(n)) at q = 0, Comm. Math. Phys., 136 (1991), 543-566.
17. V. G. Kac, Infinite dimensional Lie algebras, 3rd ed., CUP, Cambridge, 1990.
18. M. Kashiwara, On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. J., 63 (1991), 465-516.
19. A. Kleshchev, Branching rules for the modular representations of symmetric groups III: some corollaries and a problem of Mullineux, J. London Math. Soc. (2), 54 (1996), 25-38.
20. A. Lascoux, B. Leclerc, J.-Y. Thibon, Hecke algebras at roots of unity and crystal bases of quantum affine algebras, Comm. Math. Phys., 181 (1996), 205-263.
21. G. Lusztig, Introduction to Quantum Groups, Progress in mathematics, 110, Birkhäuser, Boston, 1993.
22. A. Mathas, Simple modules of Ariki-Koike algebras, Proc. Sym. Pure Math., 63, 1998, 383-396.
23. q(sl(n)), Comm. Math. Phys., 134 (1990), 79-88.
24. J.D. Rogawski, Representations of GL(n) over a p-adic field with an Iwahori-fixed vector, Israel J. Math. 54 (1986), 242-256.
25. M-F. Vigneras, Induced R-representations of p-adic reductive groups, Selecta Math., to appear.
26. M-F. Vigneras, Représentations l-modulaires d'un groupe réductif p-adique avec l ≠ p, Prog. in Math. 137, (1996), Birkhäuser.
27. M-F. Vigneras, A propos d'une conjecture de Langlands modulaire, Finite Reductive Groups, related structures and representations, M. Cabanes eds., (Luminy, 1994), Prog. in Math. 141, Birkhäuser.
28. M-F. Vigneras, private communication.