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The Cuspidal Modules of the Finite General Linear Groups

Published online by Cambridge University Press:  01 February 2010

D.I. Deriziotis  and
C.P. Gotsis
D.I. Deriziotis
Affiliation:
Department of Mathematics, University of Athens, Panepistemiopolis, Athens, Greece. dderiz@eudoxos.dm.uoa.gr, cgotsis@eudoxos.dm.uoa.gr
C.P. Gotsis
Affiliation:
Department of Mathematics, University of Athens, Panepistemiopolis, Athens, Greece. dderiz@eudoxos.dm.uoa.gr, cgotsis@eudoxos.dm.uoa.gr

Abstract

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In this paper we prove a conjecture due to R. Carter [2], concerning the action of the finite general linear group GLn(q) on a cuspidal module. As an application of this result, we work out the caseGL4(q).

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 1 , 1998 , pp. 75 - 108
Copyright
Copyright © London Mathematical Society 1998

References

references

1. Carter, R.W., Finite groups of Lie-type conjugacy classes and complex characters (Wiley, New York, 1985).Google Scholar
2. Carter, R.W., ‘Cuspidal matrix representations for GL2(q) and GL3(q)’, Proc. London Math. Soc. (3) 64 (1992) 487–523.CrossRefGoogle Scholar
3. Curtis, C.W. and Reiner, I., Methods of representation theory with applications to finite groups and orders, Vol. 1 (Wiley, New York, 1981).Google Scholar
4. Deligne, P. and Lusztig, G., ‘Representations of reductive groups over finite fields’, Ann. of Math. 103 (1976) 103–161.CrossRefGoogle Scholar
5. Green, J.A., ‘The characters of the finite general linear groups’, Trans. Amer. Math. Soc. 80 (1955) 402–447.CrossRefGoogle Scholar
6. Gotsis, C., ‘Complex representations of the general linear gGroup GLn(q)’, Ph.D. Thesis, Athens University (1997).Google Scholar
7. Fleischmann, P. and Janiszczak, I., ‘The number of regular semisimple elements for Chevalley groups of Classical type’, J. of Algebra 155 (1993) 482–528.CrossRefGoogle Scholar
8. Helversen-Pasotto, A., ‘Darstellungen von GL(3, Fq) und GauΩsche Summen’, Math. Ann. 260 (1982) 1–21.CrossRefGoogle Scholar
9. Piatetski-Shapiro, I., ‘Complex representations of GL(2, K) for finite fields K’, Contemporary Mathematics 16 (Amer. Math. Soc., Providence, R. I, 1983).CrossRefGoogle Scholar
10. Seminar, T. Springer, D Seminar on algebraic groups and related finite groups, Lecture Notes in Mathematics 131 (ed.Borel, A. et al. , Springer-Verlag, Berlin, 1970).Google Scholar