Mathematics

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

Andrew Katson '25, Illinois Mathematics and Science Academy

9:20 AM - 9:35 AM

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 ).