Characterizing the H-Orbit Decomposition of the Symmetric Spaces for the Special Orthogonal Group Over a Finite Field in Dimension 3

Session Number

Project ID: MATH 01

Advisor(s)

Ellen Ziliak, Benedictine University

Discipline

Mathematics

Start Date

17-4-2024 9:20 AM

End Date

17-4-2024 9:35 AM

Abstract

In this paper, we characterize the General and Extended Symmetric Spaces of the Special Orthogonal Group of 3 by 3 matrices over a finite field. Specifically, we use the fixed point group H to partition the sets of matrices that are unipotent, semisimple, or both in the Generalized Symmetric Spaces of SO(3, F q ).

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Apr 17th, 9:20 AM Apr 17th, 9:35 AM

Characterizing the H-Orbit Decomposition of the Symmetric Spaces for the Special Orthogonal Group Over a Finite Field in Dimension 3

In this paper, we characterize the General and Extended Symmetric Spaces of the Special Orthogonal Group of 3 by 3 matrices over a finite field. Specifically, we use the fixed point group H to partition the sets of matrices that are unipotent, semisimple, or both in the Generalized Symmetric Spaces of SO(3, F q ).