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ON THE RESTRICTION OF CHARACTERS OF STEINBERG–TITS TRIALITY GROUP 3D4(q) ON UNIPOTENT CLASSES

Published online by Cambridge University Press:  01 September 2009

VAHID DABBAGHIAN
VAHID DABBAGHIAN*
Affiliation:
The IRMACS Centre, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada e-mail: [email protected]
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Abstract

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Let G be a finite Steinberg–Tits triality group 3D4(q), and let H be a maximal unipotent subgroup of G. In this paper we classify irreducible characters χ of G such that χH has a linear constituent with multiplicity one.

Keywords

Primary 20C15secondary 20C33
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 467 - 471
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Dabbaghian-Abdoly, V., An algorithm to construct representations of finite groups, PhD thesis (School of Mathematics, Carleton University, 2003).Google Scholar
2.Dabbaghian-Abdoly, V., Characters of some finite groups of Lie type with a restriction containing a linear character once, J. Algebra 309 (2007), 543–558.CrossRefGoogle Scholar
3.Dabbaghian-Abdoly, V., Constructing representations of the finite symplectic group Sp(4, q), J. Algebra 303 (2006), 618–625.Google Scholar
4.Deriziotis, D. I. and Michler, G. O., Character table and blocks of finite simple triality groups 3D 4(q), Trans. Am. Math. Soc. 303 (1) (1987), 39–70.Google Scholar
5.Dixon, J. D., Constructing representations of finite groups, Discrete Mathematics and Theoretical Computer Science 11 (American Mathematical Society, Providence, RI 1993).Google Scholar
6.Geck, M., Hiss, G., Lübeck, F., Malle, G. and Pfeiffer, G., CHEVIE: A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras, Appl. Algebra Eng. Comm. Comput. 7 (1996), 175–210. Available at “http://www.math.rwth-aachen.de/~CHEVIE”.Google Scholar
7.Gelfand, I. M. and Graev, M. I., Construction of irreducible representations of simple algebraic groups over a finite field, Dokl. Akad. Nauk SSSR 147 (1962), 529–532.Google Scholar
8.Isaacs, I. M., Characters of π -separable groups, J. Algebra 86 (1984), 98–128.CrossRefGoogle Scholar
9.Janusz, G. J., Primitive idempotents in group algebras, Proc. Am. Math. Soc. 17 (1966), 520–523.CrossRefGoogle Scholar
10.Kawanaka, N., Generalized Gel'fand Graev representations and Ennola duality, Advanced Studies in Pure Mathematics 6 (North-Holland, Amsterdam, 1985).Google Scholar
11.Ohmori, Z., On a Zelevinsky theorem and the Schur indices of the finite unitary groups, J. Math. Sci. Univ. Tokyo 4 (1997), 417–433.Google Scholar
12.Spaltenstein, N., Caractres unipotents de 3D 4(Fq), Comment. Math. Helv. 57 (4) (1982), 676–691.Google Scholar
13.Steinberg, R., Lectures on Chevalley groups (Yale University, New Haven, 1968).Google Scholar
14.Turull, A., Calculating Clifford classes for characters containing a linear character once, J. Algebra, 254 (2002), 264–278.CrossRefGoogle Scholar
15.Zelevinsky, A. V., Representations of finite classical groups, Lecture Notes in Mathematics 869 (Springer, New York, 1981).Google Scholar