On the structure of generalized symmetric spaces of SLnš½q)
Catherine A. Buell, Aloysius G. Helminck, Vicky Williams Klima, Jennifer B. Schaefer, Carmen Wright, Ellen M Ziliak Ā· Communications in Algebra Ā· 2017
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.