Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

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 95j:20036
  • 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 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 $BN$-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 $BN$-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 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 $p$-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 $BN$-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
MSC (2000): Primary 20C08, 20F36, 20F55; Secondary 57M27
Published electronically: December 27, 2001
Review copyright: © Copyright 2001 American Mathematical Society
American Mathematical Society