On the structure of generalized symmetric spaces of SLn𝔽q). Issue 12 (2nd December 2017) - Buell, C.; Helminck, A.; Klima, V.; Schaefer, J.; Wright, C.; Ziliak, E.
ABSTRACT: 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 SL n ( k ) for any integer n >2. Specifically, we discuss the generalized and extended symmetric spaces of SL n ( 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.