Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

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

References [Enhancements On Off] (What's this?)

1.
H. H. Andersen, J. C. Jantzen and W. Soergel, Representations of quantum groups at a $p$th root of unity and of semisimple groups in characteristic $p$: independence of $p$, Astérisque 220 (1994). MR 1272539
2.
S. Ariki, On the decomposition numbers of the Hecke algebra of $G(r,p,n)$, J. Math. Kyoto Univ. 36 (1996), 789-808. MR 1443748
3.
J. S. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993), 253-287. MR 1191478
4.
N. Bourbaki, Groupes et algèbres de Lie, Chapters 4-6, Hermann, Paris (1968). MR 0240238
5.
E. Brieskorn and K. Saito, Artin-Gruppen and Coxeter-Gruppen, Invent. Math. 17 (1972), 245-271. MR 0323910
6.
M. Broué and G. Malle, Zyklotomische Heckealgebren, Astérisque 212 (1993), 119-189. MR 1235834
7.
M. Broué, G. Malle and R. Rouquier, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998), 127-190. MR 1637497
8.
M. Broué, G. Malle and J. Michel, Towards Spetses I, Transform. Groups 4 (1999), 157-218. MR 1712862
9.
R. W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1-59. MR 0318337
10.
R. W. Carter, Finite groups of Lie type: Conjugacy classes and complex characters, Wiley Classics Library Edition (1993). MR 1266626
11.
C. W. Curtis, N. Iwahori and R. W. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with $BN$-pairs, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 81-116. MR 0347996
12.
C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Wiley Classics Library Edition (1988). MR 1013113
13.
P. Deligne, Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972), 273-302. MR 0422673
14.
M. Geck, On the character values of Iwahori-Hecke algebras of exceptional type, Proc. London Math. Soc. (3) 68 (1994), 51-76. MR 1243835
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 1685620
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 1486215
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 1425324
19.
M. Geck and G. Pfeiffer, On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79-94. MR 1250466
20.
P. N. Hoefsmit, Representations of Hecke algebras of finite groups with $BN$-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 0570873
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 0165016
23.
D. A. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 0560412
24.
D. A. Kazhdan and G. Lusztig, Schubert varieties and Poincaré duality, Proc. Sympos. Pure Math. 34 (1980), 185-203. MR 0573434
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 1410572
26.
G. Lusztig, A class of irreducible representations of a Weyl group, Indag. Math. 41 (1979), 323-335. MR 0546372
27.
G. Lusztig, On a theorem of Benson and Curtis, J. Algebra 71 (1981), 490-498. MR 0630610
28.
G. Lusztig, Intersection cohomology methods in representation theory, Proc. Int. Cong. Math. Kyoto, Japan 1990, Springer-Verlag (1991), 155-174. MR 1159211
29.
G. Lusztig, Classification of unipotent representations of simple $p$-adic groups, Int. Math. Res. Notices 11 (1995), 517-589. MR 1369407
30.
I. G. Macdonald, Some irreducible representations of Weyl groups, Bull. London Math. Soc. 4 (1972), 148-150. MR 0320171
31.
H. Matsumoto, Générateurs et relations des groupes de Weyl généralisés, C. R. Acad. Sci. Paris 258 (1964), 3419-3422. MR 0183818
32.
A. J. Starkey, Characters of the generic Hecke algebra of a system of $BN$-pairs, Ph.D. thesis, University of Warwick (1975).
Review Information:

Reviewer: Roger W. Carter
Affiliation: University of Warwick
Email: rwc@maths.warwick.ac.uk
Journal: Bull. Amer. Math. Soc. 39 (2002), 267-272
Published electronically: December 27, 2001
Review copyright: © Copyright 2001 American Mathematical Society