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Book Information

Author(s): Meinolf Geck and Götz Pfeiffer
Title: Characters of finite Coxeter groups and Iwahori-Hecke algebras
Additional book information: Oxford University Press, 2000, xv + 443, $110.00, 0-19-850250-8

1.: H. H. Andersen, J. C. Jantzen and W. Soergel, Representations of quantum groups at a th root of unity and of semisimple groups in characteristic : independence of , Astérisque 220 (1994). MR 95j:20036
2.: S. Ariki, On the decomposition numbers of the Hecke algebra of , J. Math. Kyoto Univ. 36 (1996), 789-808. MR 98h:20012
3.: J. S. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993), 253-287. MR 94b:57007
4.: N. Bourbaki, Groupes et algèbres de Lie, Chapters 4-6, Hermann, Paris (1968). MR 39:1590
5.: E. Brieskorn and K. Saito, Artin-Gruppen and Coxeter-Gruppen, Invent. Math. 17 (1972), 245-271. MR 48:2263
6.: M. Broué and G. Malle, Zyklotomische Heckealgebren, Astérisque 212 (1993), 119-189. MR 94m:20095
7.: M. Broué, G. Malle and R. Rouquier, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998), 127-190. MR 99m:20088
8.: M. Broué, G. Malle and J. Michel, Towards Spetses I, Transform. Groups 4 (1999), 157-218. MR 2001b:20082
9.: R. W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1-59. MR 47:6884
10.: R. W. Carter, Finite groups of Lie type: Conjugacy classes and complex characters, Wiley Classics Library Edition (1993). MR 94k:20020
11.: C. W. Curtis, N. Iwahori and R. W. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with -pairs, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 81-116. MR 50:494
12.: C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Wiley Classics Library Edition (1988). MR 90g:16001
13.: P. Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972), 273-302. MR 54:10659
14.: M. Geck, On the character values of Iwahori-Hecke algebras of exceptional type, Proc. London Math. Soc. (3) 68 (1994), 51-76. MR 94i:20073
15.: M. Geck, Beiträge zur Darstellungstheorie von Iwahori-Hecke Algebren, Aachener Beitr. Math. Vol. 11, Aachen (1995).
16.: M. Geck, Representations of Hecke algebras at roots of unity, Astérisque 252 (1998), 33-55. MR 2000g:20018
17.: M. Geck, G. Hiss, F. Lübeck, G. Malle and G. Pfeiffer, CHEVIE--A system for computing and processing generic character tables, Appl. Algebra Engrg. Comm. Comput. 7 (1996), 175-210. MR 99m:20017
18.: M. Geck and J. Michel, ``Good'' elements in finite Coxeter groups and representations of Iwahori-Hecke algebras, Proc. London Math. Soc. (3) 74 (1997), 275-305. MR 97i:20050
19.: M. Geck and G. Pfeiffer, On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79-94. MR 94m:20018
20.: P. N. Hoefsmit, Representations of Hecke algebras of finite groups with -pairs of classical type, Ph.D. thesis, University of British Columbia, Vancouver (1974).
21.: R. B. Howlett and G. I. Lehrer, Induced cuspidal representations and generalized Hecke rings, Invent. Math. 58 (1980), 37-64. MR 81j:20017
22.: N. Iwahori, On the structure of the Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. IA 10 (1964), 215-236. MR 29:2307
23.: D. A. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 81j:20066
24.: D. A. Kazhdan and G. Lusztig, Schubert varieties and Poincaré duality, Proc. Sympos. Pure Math. 34 (1980), 185-203. MR 84g:14054
25.: A. Lascoux, B. Leclerc and J. Y. Thibon, Hecke algebras at roots of unity and crystal bases of quantum affine algebras, Comment. Math. Phys. 181 (1996), 205-263. MR 97k:17019
26.: G. Lusztig, A class of irreducible representations of a Weyl group, Indag. Math. 41 (1979), 323-335. MR 81a:20052
27.: G. Lusztig, On a theorem of Benson and Curtis, J. Algebra 71 (1981), 490-498. MR 83a:20053
28.: G. Lusztig, Intersection cohomology methods in representation theory, Proc. Int. Cong. Math. Kyoto, Japan 1990, Springer-Verlag (1991), 155-174. MR 93e:20059
29.: G. Lusztig, Classification of unipotent representations of simple -adic groups, Int. Math. Res. Notices 11 (1995), 517-589. MR 98b:22034
30.: I. G. Macdonald, Some irreducible representations of Weyl groups, Bull. London Math. Soc. 4 (1972), 148-150. MR 47:8710
31.: H. Matsumoto, Générateurs et relations des groupes de Weyl généralisés, C. R. Acad. Sci. Paris 258 (1964), 3419-3422. MR 32:1294
32.: A. J. Starkey, Characters of the generic Hecke algebra of a system of -pairs, Ph.D. thesis, University of Warwick (1975).

Reviewer(s):
Roger W. Carter
Affiliation: University of Warwick
Email: rwc@maths.warwick.ac.uk

MSC (2000): Primary 20C08, 20F36, 20F55; Secondary 57M27
DOI: 10.1090/S0273-0979-01-00931-4
PII: S 0273-0979(01)00931-4
Posted: December 27, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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