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On the structure of generalized symmetric spaces of SLn𝔽q) |
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| Authors: | C Buell A Helminck V Klima C Wright E Ziliak |
| Institution: | 1. Department of Mathematics, Fitchburg State University, Fitchburg, Massachusetts, USA;2. College of Natural Sciences, University of Hawaii at Manoa, Honolulu, Hawaii, USA;3. Department of Mathematical Sciences, Appalachian State University, Boone, North Carolina, USA;4. Department of Mathematical and Statistical Sciences, Jackson State University, Jackson, Mississippi, USA;5. Department of Mathematical and Computational Sciences, Benedictine University, Lisle, Illinois, USA |
| 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 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. |
| Keywords: | Finite fields generalized symmetric space special linear group |