On the structure of Generalized Symmetric Spaces of
} and ![\bm{\mbox{GL}_{2}(\mathbb{F}_{\MakeLowercase{q}})}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/c1c01f9e9a7b7bdaaffa1d0fce73c7f7.png)
Abstract
In this paper we will discuss the generalized symmetric spaces for
and
. Specifically we will characterize the structure of these spaces and prove that when the characteristic of
is not equal to two the extended generalized symmetric space is equal to the generalized symmetric space for
and nearly equal for
for all but one involution.
![\SL_2(\mathbb{F}_q)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/816f3a0455faf2fdff72f50d0aadde3f.png)
![\GL_2(\mathbb{F}_q)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/3edb41184157d9b47720e5ef1a009afd.png)
![\mathbb{F}_q](https://853417.krfdn.asia/plugins/generic/latexRender/cache/6d2b4c3c1671bd7647831bd61e2b9f68.png)
![\SL_2(\mathbb{F}_q)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/816f3a0455faf2fdff72f50d0aadde3f.png)
![\GL_2(\mathbb{F}_q)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/3edb41184157d9b47720e5ef1a009afd.png)
DOI Code:
10.1285/i15900932v37n2p1
Keywords:
generalized symmetric space; special linear group; nite elds
Full Text: PDF