Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-14T18:29:10.476Z Has data issue: false hasContentIssue false
  • English
  • Français

The reflection character of $D_n(q)$

Published online by Cambridge University Press:  24 February 2005

ANTHONY C. KABLE  and
NILABH SANAT
ANTHONY C. KABLE
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater OK 74078, U.S.A. e-mail: akable@math.okstate.edu and nilabh.sanat@wku.edu
NILABH SANAT
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater OK 74078, U.S.A. e-mail: akable@math.okstate.edu and nilabh.sanat@wku.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We evaluate the character of the reflection representation of the split special orthogonal group over a finite field $F$ of odd characteristic. The value of the character at $g$ is expressed in terms of the dimensions of the eigenspaces of $g$ for eigenvalues in $F$ and in the norm 1 torus in the quadratic extension of $F$, and the behavior of the restriction of the quadratic form preserved by the group to the 1 and ${-}1$ eigenspaces of $g$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 138 , Issue 2 , March 2005 , pp. 193 - 210
Copyright
2005 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)