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Constructible characters, leading coefficients and left cells for finite Coxeter groups with unequal parameters


Author: Meinolf Geck
Journal: Represent. Theory 6 (2002), 1-30
MSC (2000): Primary 20C08; Secondary 20C15
DOI: https://doi.org/10.1090/S1088-4165-02-00128-0
Published electronically: March 27, 2002
MathSciNet review: 1915085
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Abstract: Following Lusztig, we investigate constructible characters, leading coefficients and left cells for a finite Coxeter group $W$ in the case of unequal parameters. We obtain explicit results for $W$ of type $F_4$, $B_n$ and $I_2(m)$ ($m$ 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.


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  • 1. D. ALVIS, The left cells of the Coxeter group of type ${H}_4$, 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 ${H}_4$, 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 $({{\mathbb{Z} }}/r{{\mathbb{Z} }}) \wr {{\mathfrak{S}}}_n$ 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 $B_n$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/$\sim$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 $B_n$ 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

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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: https://doi.org/10.1090/S1088-4165-02-00128-0
Received by editor(s): June 8, 2001
Received by editor(s) in revised form: November 7, 2001
Published electronically: March 27, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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