Visualizing Random Walks on Supercharacter Theories for Uppertriangular Unipotent Matrices
Justin Willson · CU Scholar (University of Colorado Boulder) · 2019
The conjugacy classes of some finite groups are provably wild in the sense that there is no general solution to finding their conjugacy classes other than brute force. One solution to this problem is to create a supercharacter theory for a group which has the effect of gluing together conjugacy classes into more manageable chunks. In this paper we apply these methods to the group of uppertriangular unipotent matrices and analyze the combinatorics of this added structure.