Reduction for characters of finite algebra groups

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 x n matrices over F-q. Using our procedure, we compute the number of irreducible characters of U-n(q) of each degree for n <= 13. Also, we explain and generalise a phenomenon concerning the group U-13(2) discovered by Isaacs and Karagueuzian. (C) 2010 Elsevier Inc. All rights reserved.