Reduction for characters of finite algebra groups

TL;DR

This paper introduces a new procedure for analyzing characters of finite algebra groups, specifically focusing on unipotent upper triangular matrices over finite fields, and computes their irreducible characters for small n.

Contribution

It formulates a novel method for character analysis of finite algebra groups and generalizes a known phenomenon related to unipotent groups.

Findings

Computed the number of irreducible characters of U_n(q) for n<14

Generalized a phenomenon observed in U_{13}(2)

Provided a systematic procedure for character analysis

Abstract

Let J be a finite-dimensional nilpotent algebra over a finite field F_q. We formulate a procedure for analysing characters of the group 1+J. In particular, we study characters of the group $U_n (q)$ of unipotent triangular $n\times n$ matrices over F_q. Using our procedure, we compute the number of irreducible characters of $U_n (q)$ of each degree for n<14. Also, we explain and generalise a phenomenon concerning the group $U_{13}(2)$ discovered by Isaacs and Karagueuzian.