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Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents
-
Rod Gow
Published/Copyright:
May 21, 2008
Abstract
Let GL
and U
denote the finite general linear and unitary groups extended by the transpose inverse automorphism, respectively, where q is a power of the prime p. Let n be odd, and let χ be an irreducible character of either of these groups which is an extension of a real-valued character of GL
or U
. Let yτ be an element of GL or U such that (yτ)2 is regular unipotent in GL or U, respectively. We show that 
is prime to p and 
otherwise. Several intermediate results on real conjugacy classes and real-valued characters of these groups are obtained along the way.
Received: 2007-05-04
Revised: 2007-07-10
Published Online: 2008-05-21
Published in Print: 2008-May
© de Gruyter 2008
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- Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents
- Involution models of finite Coxeter groups
- Prime divisors of character degrees
- A characterization of HN
- Symmetric groups and conjugacy classes
- Conjugacy classes of non-normal subgroups in finite nilpotent groups
- Normalizers of subgroups of division rings
- On the Frattini and upper near Frattini subgroups of a generalized free product
- Reflection principle characterizing groups in which unconditionally closed sets are algebraic
Articles in the same Issue
- Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents
- Involution models of finite Coxeter groups
- Prime divisors of character degrees
- A characterization of HN
- Symmetric groups and conjugacy classes
- Conjugacy classes of non-normal subgroups in finite nilpotent groups
- Normalizers of subgroups of division rings
- On the Frattini and upper near Frattini subgroups of a generalized free product
- Reflection principle characterizing groups in which unconditionally closed sets are algebraic
