On the structure of generalized symmetric spaces of SLn𝔽q). Issue 12 (2nd December 2017)

• Record Type: Journal Article
• Authors: Buell, C.; Helminck, A.; Klima, V.; Schaefer, J.; Wright, C.; Ziliak, E.
• Is Part Of: Communications in algebra. Volume 45:Issue 12(2017)
• Page Start: 5123
• Page End: 5136
• Publication Date: 2017-12-02
• Subjects: Finite fields -- generalized symmetric space -- special linear group; 20G40 -- 22E46 -- 53C35 -- 57S20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1296458
• Languages: English
• ISSNs: 0092-7872

Abstract

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.