Involutions and characters of upper triangular matrix groups

Authors:
I. M. Isaacs and Dikran B. Karagueuzian

Journal:
Math. Comp. **74** (2005), 2027-2033

MSC (2000):
Primary 20C15; Secondary 20D15

Published electronically:
March 24, 2005

MathSciNet review:
2164110

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the realizability over of representations of the group of upper-triangular matrices over . We prove that all the representations of are realizable over if , but that if , has representations not realizable over . This theorem is a variation on a result that can be obtained by combining work of J. Arregi and A. Vera-López and of the authors, but the proof of the theorem in this paper is much more natural.

**1.**John Cannon and Derek Holt (eds.),*Computational algebra and number theory*, Elsevier Ltd, Oxford, 1997. J. Symbolic Comput. 24 (1997), no. 3-4. MR**1484477****2.**J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson,*Atlas of finite groups*, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR**827219****3.**Charles W. Curtis and Irving Reiner,*Methods of representation theory. Vol. I*, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1990. With applications to finite groups and orders; Reprint of the 1981 original; A Wiley-Interscience Publication. MR**1038525****4.**Isaacs, I. M.,*Character Theory of Finite Groups*, Dover (1994).**5.**I. M. Isaacs and Dikran Karagueuzian,*Conjugacy in groups of upper triangular matrices*, J. Algebra**202**(1998), no. 2, 704–711. MR**1617655**, 10.1006/jabr.1997.7311**6.**I. M. Isaacs and Dikran Karagueuzian,*Erratum: “Conjugacy in groups of upper triangular matrices” [J. Algebra 202 (1998), no. 2, 704–711; MR1617655 (99b:20011)]*, J. Algebra**208**(1998), no. 2, 722. MR**1655475**, 10.1006/jabr.1998.7430**7.**Michael C. Slattery,*Computing character degrees in 𝑝-groups*, J. Symbolic Comput.**2**(1986), no. 1, 51–58. MR**839136**, 10.1016/S0747-7171(86)80012-8**8.**Antonio Vera López and Jesus Maria Arregi,*Conjugacy classes in Sylow 𝑝-subgroups of 𝐺𝐿(𝑛,𝑞)*, J. Algebra**152**(1992), no. 1, 1–19. MR**1190401**, 10.1016/0021-8693(92)90085-Z**9.**Vera López, A. and Arregi, J., private communication.

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Additional Information

**I. M. Isaacs**

Affiliation:
Mathematics Department, University of Wisconsin at Madison, Madison, Wisconsin 53706

Email:
isaacs@math.wisc.edu

**Dikran B. Karagueuzian**

Affiliation:
Mathematics Department, Binghamton University, Binghamton, New York, 13902-6000

Email:
dikran@math.binghamton.edu

DOI:
http://dx.doi.org/10.1090/S0025-5718-05-01705-9

Keywords:
Character theory,
finite groups,
p-groups

Received by editor(s):
August 6, 2002

Received by editor(s) in revised form:
February 24, 2004

Published electronically:
March 24, 2005

Additional Notes:
The research of the second author was partially supported by an N.S.F. Postdoctoral Fellowship, the MPIM-Bonn, and the CRM-Barcelona.

Article copyright:
© Copyright 2005
American Mathematical Society