On the structure of Generalized Symmetric Spaces of $\bm{\mbox{SL}_{2}(\mathbb{F}_{\MakeLowercase{q}})}$} and $\bm{\mbox{GL}_{2}(\mathbb{F}_{\MakeLowercase{q}})}$

Authors

  • C. Buell
  • A. G. Helminck
  • V. Klima
  • J. Schaefer
  • C. Wright
  • E. Ziliak

DOI:

https://doi.org/10.1285/i15900932v37n2p1

Keywords:

generalized symmetric space, special linear group, nite elds

Abstract

In this paper we will discuss the generalized symmetric spaces for $\SL_2(\mathbb{F}_q)$ and $\GL_2(\mathbb{F}_q)$. Specifically we will characterize the structure of these spaces and prove that when the characteristic of $\mathbb{F}_q$ is not equal to two the extended generalized symmetric space is equal to the generalized symmetric space for $\SL_2(\mathbb{F}_q)$ and nearly equal for $\GL_2(\mathbb{F}_q)$ for all but one involution.

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Published

15-02-2018

Issue

Volume 37, Issue 2 (2017)

Section

Articoli

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