On the structure of Generalized Symmetric Spaces of  } and

doi:10.1285/i15900932v37n2p1

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

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

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.

DOI Code: 10.1285/i15900932v37n2p1

Keywords: generalized symmetric space; special linear group; nite elds

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On the structure of Generalized Symmetric Spaces of } and

Abstract

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