Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Dade's invariant conjecture for general linear and unitary groups in non-defining characteristics


Author: Jianbei An
Journal: Trans. Amer. Math. Soc. 353 (2001), 365-390
MSC (2000): Primary 20C20, 20G40
DOI: https://doi.org/10.1090/S0002-9947-00-02580-0
Published electronically: September 13, 2000
MathSciNet review: 1707189
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups.

The invariant conjecture of Dade is proved for general linear and unitary groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.


References [Enhancements On Off] (What's this?)

  • [1] J. L. Alperin, Large abelian subgroups of $p$-groups, Trans. Amer. Math. Soc. 117 (1965), 10-20. MR 30:180
  • [2] J. L. Alperin and P. Fong, Weights for symmetric and general linear groups, J. Algebra 131 (1990), 2-22. MR 91h:20014
  • [3] Jianbei An, Weights for classical groups, Trans. Amer. Math. Soc. 342 (1994), 1-42. MR 94e:20015
  • [4] M. Broué, Les $\ell $-blocs des groupes $\mathrm{GL}(n,q)$et $\mathrm{U}(n,q^{2})$ et leurs structures locales, Séminaire Bourbaki Astérisque 133-134 (1986), 159-188.MR 87e:20021
  • [5] M. Broué, Isométries parfaites, types de blocs, catégories dérivées. Astérisque 181-182 (1990), 61-92. MR 91i:20006
  • [6] E. Dade, Counting characters in blocks, I, Invent. Math. 109 (1992), 187-210. MR 93g:20021
  • [7] E. Dade, Counting characters in blocks, II.9. in Representation Theory of Finite Groups (R. Solomon, editor), Ohio State University Math. Res. Inst. Publ. 6, de Gruyter, Berlin 1997.MR 99b:20016
  • [8] E. Dade, Counting characters in blocks with cyclic defect groups, I, J. Algebra 186 (1996), 934-969. MR 98b:20013
  • [9] W. Feit, The representation theory of finite groups, North Holland, 1982. MR 83g:20001
  • [10] P. Fong and B. Srinivasan, The blocks of finite general linear and unitary groups, Invent. Math. 69 (1982), 109-153. MR 3k:20013
  • [11] G. O. Michler and J. B. Olsson, Character correspondences in finite general linear, unitary and symmetric groups, Math. Z. 184 (1983), 203-233.MR 85e:20014
  • [12] J. B. Olsson, On the number of characters in blocks of finite general linear, unitary and symmetric groups, Math. Z. 186 (1984), 41-47. MR 85d:20008
  • [13] J. B. Olsson and K. Uno, Dade's conjecture for general linear groups in the defining characteristic, Proc. London Math. Soc. 72 (1996), 359-384. MR 97b:20010
  • [14] J. B. Olsson and K. Uno, Dade's conjecture for symmetric groups, J. Algebra 176 (1995), 534-560.MR 96h:20025

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20C20, 20G40

Retrieve articles in all journals with MSC (2000): 20C20, 20G40


Additional Information

Jianbei An
Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
Email: an@math.auckland.ac.nz

DOI: https://doi.org/10.1090/S0002-9947-00-02580-0
Received by editor(s): August 28, 1998
Received by editor(s) in revised form: February 5, 1999, and June 16, 1999
Published electronically: September 13, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society