A New Subgroup Chain for the Finite Affine Group

• Main Author: Lingenbrink, David Alan, Jr.
• Format: Others
• Published: Scholarship @ Claremont 2014
• Subjects: 65T50 Discrete and fast Fourier transforms; 20G05 Representation theory; 20H20 Other matrix groups over fields; Algebra; Harmonic Analysis and Representation
• Online Access: http://scholarship.claremont.edu/hmc_theses/55; http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1064&context=hmc_theses

The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.