On the representation theory of iwahori–hecke algebras of extended finite weyl groups

Representation Theory

Volumn 4, Issue 15, 2000, Pages 370-397

  Geck, Meinolf ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85009814728     PISSN: 10884165     EISSN: None     Source Type: Journal    
DOI: 10.1090/S1088-4165-00-00093-5     Document Type: Article

References (34)

1. S. Ariki, On the decomposition numbers of the Hecke algebra of G(m, 1, n), J. Math. Kyoto Univ. 36 (1996), 789–808. MR 98h:20012
2. S. Ariki and A. Mathas, The number of simple modules of the Hecke algebras of type G(r, 1, n), Math. Z. 233 (2000), 601–623. CMP 2000:11
3. R. W. Carter, Finite groups of Lie type: Conjugacy classes and complex characters, Wiley, New York (1985). MR 94k:20020 (Reprint of 1985 original)
4. C. W. Curtis and I. Reiner, Methods of representation theory Vol. I and II, Wiley, New York, 1981 and 1987. MR 82i:20001; MR 88f:20002
5. F. Digne and J. Michel, Fonctions L des variétés de Deligne–Lusztig et descente de Shin-tani, Mémoire Soc. Math. France 20, 1985. MR 87h:20071
6. R. Dipper and G. D. James, Representations of Hecke algebras of the general linear groups, Proc. London Math. Soc. 52 (1986), 20–52. MR 88b:20065
7. n, J. Algebra 146 (1992), 454–481. MR 93c:20019
8. n at roots of unity, Proc. London Math. Soc. 70 (1995), 505–528. MR 96b:20004
9. W. Feit, The representation theory of finite groups, North–Holland, Amsterdam/New York/Oxford, 1982. MR 83g:20001
10. O. Foda, B. Leclerc, M. Okado, J.-Y. Thibon and T. A. Welsh, Branching functions of A (1) n − 1 and Jantzen–Seitz problem for Ariki–Koike algebras, Advances in Math. 141 (1999), 322–365. MR 2000f:17036
11. 4, Manuscripta Math. 70 (1991), 285–306. MR 92a:20043
12. M. Geck, The decomposition numbers of the Hecke algebra of type E ∗ 6, Math. Comp. 61 (1993), 889–899. MR 94f:20020
13. M. Geck, Representations of Hecke algebras at roots of unity, Séminaire Bourbaki, 50ème année, 1997-98, Astérisque No. 252 (1998), Exp. 836, 33–55. MR 2000g:20018
14. M. Geck, Kazhdan–Lusztig cells and decomposition numbers, Represent. Theory 2 (1998), 264–277 (electronic). MR 99e:20015
15. M. Geck, G. Hiss and G. Malle, Towards a classification of the irreducible representations in non-defining characteristic of a finite group of Lie type, Math. Z. 221 (1996), 353–386. MR 98a:20017
16. M. Geck and G. Pfeiffer, Characters of finite Coxeter groups and Iwahori–Hecke algebras, London Math. Soc. Monographs, New Series 21, Oxford University Press, 2000.
17. M. Geck, S, Kim and G. Pfeiffer, Minimal length elements in twisted conjugacy classes of finite Coxeter groups, J. Algebra 229 (2000), 570–600.
18. M. Geck and R. Rouquier, Filtrations on projective modules for Iwahori–Hecke algebras, preprint (1998).
19. B. Huppert, Endliche Gruppen I, Grundlehren der Math. Wiss. 134, Springer–Verlag Berlin/Heidelberg, 1967. MR 37:302
20. I. M. Isaacs, Character theory of finite groups, corrected reprint, Dover Publications, New York, 1967. CMP 94:14
21. M. Jimbo, K. C. Misra, T. Miwa and M. Okado, Combinatorics of representations of Uq(b sl(n)) at q = 0, Comm. Math. Phys. 136 (1991), 543–566. MR 93a:17015
22. D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165–184. MR 81j:20066
23. G. Lusztig, Characters of reductive groups over a finite field, Annals Math. Studies 107, Princeton University Press, 1984. MR 86j:20038
24. G. Lusztig, Cells in affine Weyl groups, Advanced Studies in Pure Math. 6, Algebraic groups and related topics, Kinokuniya and North–Holland, 1985, 255–287. MR 87h:20074
25. G. Lusztig, Cells in affine Weyl groups II, J. Algebra 109 (1987), 536–548. MR 88m:20103a
26. G. Lusztig, Cells in affine Weyl groups III, J. Fac. Sci. Univ. Tokyo 34 (1987), 223–243. MR 88m:20103b
27. G. Lusztig, Leading coefficients of character values of Hecke algebras, Proc. Symp. Pure Math. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 235–262. MR 89b:20087
28. G. Malle, Darstellungstheoretische Methoden bei der Realisierung einfacher Gruppen vom Lie–Typ als Galoisgruppen, Progress in Math. 95, pp. 443–459, Birkhäuser–Verlag, Basel, 1991. MR 93a:12005
29. G. Malle and B. H. Matzat, Inverse Galois theory, Springer Monographs in Mathematics, Springer–Verlag, Berlin, 1999. CMP 2000:02
30. A. Mathas, Simple modules of Ariki–Koike algebras, Proc. Sympos. Pure Math., 63, pp. 383–396, Amer. Math. Soc., Providence, RI, 1998. MR 99d:20018
31. H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Math. 8, Cam-bridge University Press (1986). MR 88h:13001
32. C. A. Pallikaros, Representations of Hecke algebras of type Dn, J. Algebra 169 (1994), 20–48. MR 95k:20015
33. C. A. Pallikaros, Some decomposition numbers of Hecke algebras, J. Algebra 187 (1997), 493–509. MR 97m:20022
34. I. N. Stewart and D. O. Tall, Algebraic number theory, 2nd edition, Chapman and Hall Math. Series, London/New York, 1987. MR 81d:11001