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.

**[1]**J. L. Alperin,*Large abelian subgroups of**-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**-blocs des groupes**et**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**

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