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Verifying Kottwitz' conjecture by computer
Author(s):
Bill
Casselman
Journal:
Represent. Theory
4
(2000),
32-45.
MSC (2000):
Primary 20G99
Posted:
February 1, 2000
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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  ,  ,  , and the subsidiary one for  and  . At the end I will include tables of the relevant computer output. I begin by recalling briefly what is to be computed.
References:
-
- 1.
- Dean Alvis, The left cells of the Coxeter group of type
 , J. Algebra 107 (1987), 160-168. MR 88d:20014 - 2.
- Dean Alvis and G. Lusztig, On Springer's correspondence for simple groups of type
  , 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: http://www.desargues.univ-lyon1.fr/home/geck/index.html.fr and both documentation for CHEVIE and the software itself can be found at: http://www.math.rwth-aachen.de/~CHEVIE/.
- 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: http://www.math.lsa.umich.edu/~jrs/papers.html.
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Additional Information:
Bill
Casselman
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1W5
Email:
cass@math.ubc.ca
DOI:
10.1090/S1088-4165-00-00052-2
PII:
S 1088-4165(00)00052-2
Received by editor(s):
May 14, 1998
Received by editor(s) in revised form:
October 11, 1999
Posted:
February 1, 2000
Copyright of article:
Copyright
2000,
by the author
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