On the Structure of Generalized Symmetric Spaces of SLn (��q)
Communications in Algebra
In this paper we extend previous results regarding SL2(k) over any finite field k by investigating the structure of the symmetric spaces for the family of special linear groups SLn(k) for any integer n>2. Specifically, we discuss the generalized and extended symmetric spaces of SLn(k) for all conjugacy classes of involutions over a finite field of odd or even characteristic. We characterize the structure of these spaces and provide an explicit difference set in cases where the two spaces are not equal.
Buell, C., A. Helminck, V. Klima, J. Schaefer, C. Wright, and E. Ziliak. "On the Structure of Generalized Symmetric Spaces of SLn (𝔽q)." Communications in Algebra 45, no. 12 (2017): 5123-5136. (Article published online May 11, 2017). https://www.tandfonline.com/doi/full/10.1080/00927872.2017.1296458