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Characters of  -degree with cyclotomic field of values
Authors:
Gabriel Navarro and Pham Huu Tiep
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2833-2837
MSC (2000):
Primary 20C15
Posted:
April 11, 2006
MathSciNet review:
2231605
Full-text PDF Free Access
Abstract |
References |
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Additional Information
Abstract: If  is a prime number and  is a finite group, we show that  has an irreducible complex character of degree not divisible by  with values in the cyclotomic field  .
References
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R. Carter, `Finite Groups of Lie type: Conjugacy Classes and Complex Characters', Wiley, Chichester, 1985. MR 0794307 (87d:20060)
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J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, `An ATLAS of Finite Groups', Clarendon Press, Oxford, 1985. MR 0827219 (88g:20025)
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F. Digne and J. Michel, `Representations of Finite Groups of Lie Type', London Mathematical Society Student Texts 21, Cambridge University Press, 1991. MR 1118841 (92g:20063)
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I. M. Isaacs, `Character Theory of Finite Groups', Dover, New York, 1994. MR 1280461
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I. M. Isaacs, G. Malle, and G. Navarro, Real characters of
 -degree, J. Algebra 278 (2004), 611-620. MR 2071655 (2005f:20016)
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G. Lusztig, On the representations of reductive groups with disconnected centre, in: `Orbites Unipotentes et Représentations, I.', Astérisque 168 (1988), 157-166. MR 1021495 (90j:20083)
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G. Navarro and Pham Huu Tiep, Rational irreducible characters and rational conjugacy classes in finite groups, submitted.
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Additional Information
Gabriel Navarro
Affiliation:
Facultat de Matemàtiques, Universitat de València, Burjassot, València 46100, Spain
Email:
gabriel@uv.es
Pham Huu Tiep
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email:
tiep@math.ufl.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08564-9
PII:
S 0002-9939(06)08564-9
Received by editor(s):
April 22, 2005
Posted:
April 11, 2006
Additional Notes:
The first author was partially supported by the Ministerio de Educación y Ciencia proyecto MTM2004-06067-C02-01
The second author gratefully acknowledges the support of the NSA (grant H98230-04-0066).
Communicated by:
Jonathan I. Hall
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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