Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents

Details Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents

2007-04-16

arxiv.org/abs/0704.2022v1

Mathematics

Representation Theory

27 pages

Scientific paper

When n is odd, consider the finite general linear and unitary groups of rank n, extended by the inverse transpose automorphism. There are elements in the extended groups which square to a regular unipotent element, and we evaluate the values of irreducible characters of the extended groups on these elements. Several intermediate results on real conjugacy classes and real-valued characters of these groups are obtained along the way.

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