|
Constructible characters, leading coefficients and left cells for finite Coxeter groups with unequal parameters
Author(s):
Meinolf
Geck
Journal:
Represent. Theory
6
(2002),
1-30.
MSC (2000):
Primary 20C08;
Secondary 20C15
Posted:
March 27, 2002
MathSciNet review:
1915085
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Following Lusztig, we investigate constructible characters, leading coefficients and left cells for a finite Coxeter group in the case of unequal parameters. We obtain explicit results for of type , and ( even) which support Lusztig's conjecture that known results about left cells in the equal parameter case should remain valid in the case of unequal parameters.
References:
-
- 1.
- D. ALVIS, The left cells of the Coxeter group of type
, J. Algebra 107 (1987), 160-168. MR 88d:20014 - 2.
- D. ALVIS AND G. LUSZTIG, The representations and generic degrees of the Hecke algebra of type
, J. Reine Angew. Math. 336 (1982), 201-212; corrections, ibid. 449 (1994), 217-218. MR 84a:20013; MR 84a:20013 - 3.
- S. ARIKI AND K. KOIKE, A Hecke algebra of
and construction of its irreducible representations, Adv. Math. 106 (1994), 216-243. MR 95h:20006 - 4.
- D. BARBASCH AND D. VOGAN, Primitive ideals and orbital integrals in complex exceptional groups, J. of Algebra 80 (1983), 350-382. MR 84h:22038
- 5.
- M. BROUÉ AND S. KIM, Sur les blocs de Rouquier des algèbres de Hecke cyclotomiques, preprint (October 2000).
- 6.
- R. W. CARTER, Finite groups of Lie type: Conjugacy classes and complex characters, Wiley, New York (1985). MR 87d:20060
- 7.
- C. W. CURTIS AND I. REINER, Methods of representation theory Vol. I and II, Wiley, New York, 1981 and 1987. MR 82i:20001; MR 88f:20002
- 8.
- R. DIPPER, G. D. JAMES AND G. E. MURPHY, Hecke algebras of type
at roots of unity, Proc. London Math. Soc. 70 (1995), 505-528. MR 96b:20004 - 9.
- M. GECK, G. HISS, F. L¨UBECK, G. MALLE, AND G. PFEIFFER, CHEVIE--A system for computing and processing generic character tables, Appl. Algebra Engrg. Comm. Comput. 7 (1996), 175-210; electronically available at http://www.math.rwth-aachen.de/
CHEVIE MR 99m:20017 - 10.
- M. GECK AND G. PFEIFFER, Characters of finite Coxeter groups and Iwahori-Hecke algebras, London Math. Soc. Monographs, New Series 21, Oxford University Press, 2000. CMP 2000:17
- 11.
- 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.
- 12.
- L. IANCU, Left cells in type
with unequal parameters, in preparation. - 13.
- D. KAZHDAN AND G. LUSZTIG, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 81j:20066
- 14.
- G. LUSZTIG, A class of irreducible representations of a finite Weyl group, Nederl. Akad. Wetensch. Indag. Math. 41 (1979), 323-335. MR 81a:20052
- 15.
- G. LUSZTIG, Unipotent characters of the symplectic and odd orthogonal groups over a finite field, Invent. Math. 64 (1981), 263-296. MR 83b:20011
- 16.
- G. LUSZTIG, A class of irreducible representations of a finite Weyl group II, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), 219-226. MR 83h:20018
- 17.
- G. LUSZTIG, Left cells in Weyl groups, Lie Group Representations, I (R. L. R. Herb and J. Rosenberg, eds.), Lecture Notes in Math., vol. 1024, Springer-Verlag, 1983, pp. 99-111. MR 85f:20035
- 18.
- G. LUSZTIG, Characters of reductive groups over a finite field, Annals Math. Studies 107, Princeton University Press, 1984. MR 86j:20038
- 19.
- G. LUSZTIG, Cells in affine Weyl groups, Advanced Studies in Pure Math. 6, Algebraic groups and related topics, Kinokuniya and North-Holland, 1985, 255-287. MR 87h:20074
- 20.
- G. LUSZTIG, Sur les cellules gauches des groupes de Weyl, C. R. Acad. Sci. Paris 302 (1986), 5-8. MR 87e:20089
- 21.
- G. LUSZTIG, Leading coefficients of character values of Hecke algebras, Proc. Symp. Pure Math. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 235-262. MR 89b:20087
- 22.
- G. LUSZTIG, Lectures on affine Hecke algebras with unequal parameters. Available at arXiv:math.RT/0108172.
- 23.
- R. ROUQUIER, Familles et blocs d'algèbres de Hecke, C. R. Acad. Sci. Paris, Sér. I, 329 (1999), 1037-1042. MR 2001f:20012
- 24.
- M. SCHONERT ET AL., GAP - groups, algorithms, and programming, Lehrstuhl D fur Mathematik, RWTH Aachen, Germany, fourth ed., (1994).
- 25.
- N. XI, Representations of affine Hecke algebras, Lecture Notes in Mathematics 1587, Springer-Verlag, Berlin, Heidelberg, 1994. MR 96i:20058
Similar Articles:
Retrieve articles in Representation Theory
with MSC
(2000):
20C08,
20C15
Retrieve articles in all Journals with MSC
(2000):
20C08,
20C15
Additional Information:
Meinolf
Geck
Affiliation:
Institut Girard Desargues, bat. Jean Braconnier, Université Lyon 1, 21 av Claude Bernard, F--69622 Villeurbanne Cedex, France
Email:
geck@desargues.univ-lyon1.fr
DOI:
10.1090/S1088-4165-02-00128-0
PII:
S 1088-4165(02)00128-0
Received by editor(s):
June 8, 2001
Received by editor(s) in revised form:
November 7, 2001
Posted:
March 27, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
|