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Verifying Kottwitz' conjecture by computer

Author: Bill Casselman
Journal: Represent. Theory 4 (2000), 32-45
MSC (2000): Primary 20G99
Published electronically: February 1, 2000
MathSciNet review: 1740179
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Abstract: In these notes I will discuss the computations that were used to verify the main conjecture of Kottwitz (1997) for the groups $E_{6}$, $E_{7}$, $E_{8}$, and the subsidiary one for $F_{4}$ and $E_{6}$. At the end I will include tables of the relevant computer output. I begin by recalling briefly what is to be computed.

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  • 1. Dean Alvis, The left cells of the Coxeter group of type $H_{4}$, J. Algebra 107 (1987), 160-168. MR 88d:20014
  • 2. Dean Alvis and G. Lusztig, On Springer's correspondence for simple groups of type $E_{n}$ $(n=6,\,7,\,8)$, Math. Proc. Cambridge Philos. Soc. 92 (1982), 65-78. MR 83k:20040
  • 3. N. Bourbaki, Groupes et algebres de Lie, vols. IV-VI, Hermann, Paris, 1970.
  • 4. Brigitte Brink and Robert Howlett, A finiteness property and an automatic structure for Coxeter groups, Math. Ann. 296 (1993), 179-190. MR 94d:20045
  • 5. R. W. Carter, Conjugacy classes in the Weyl group, Comp. Math. 25 (1972), 1-59. MR 47:6884
  • 6. R. W. Carter, Finite groups of Lie type, Wiley, 1985. MR 87d:20060
  • 7. W. A. Casselman, Automata to perform basic calculations in Coxeter groups, Representations of groups, CMS Conference Proceedings (published by the AMS), vol. 16, 1995, pp. 35-58. MR 96i:20050
  • 8. Fokko du Cloux, A transducer approach to Coxeter groups, J. Symbolic Comput. 27 (1999), no. 3, 311-324. MR 99k:20084
  • 9. M. Geck, G. Hiss, F. Lübeck, G. Malle, and G. Pfeiffer, CHEVIE--A system for computing and processing generic character tables, IWR Preprint 95-05, Universität Heidelberg (1995). Geck's home page is at: and both documentation for CHEVIE and the software itself can be found at:
  • 10. R. Kottwitz, Involutions in Weyl groups, Represent. Theory 4 (2000), 1-15.
  • 11. G. Lusztig, Characters of reductive groups over a finite field, Annals of Math. Studies 107, Princeton, 1984. MR 86j:20038
  • 12. G. Lusztig, Leading coefficients of character values of Hecke algebras, Proc. Symp. Pure Math. 47 (1987), 235-262. MR 89b:20087
  • 13. E.M. Opdam, A remark on the irreducible characters and fake degrees of finite real reflection groups, Invent. Math. 120 (1995), 447-454. MR 96e:20011
  • 14. John Stembridge, Computational aspects of root systems, Coxeter groups, and Weyl characters, RIMS, preprint #1216. Available at:

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Additional Information

Bill Casselman
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1W5

Received by editor(s): May 14, 1998
Received by editor(s) in revised form: October 11, 1999
Published electronically: February 1, 2000
Article copyright: © Copyright 2000 by the author

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