The regular character of the unitriangular group (Q1268087)

Let \(U_n(q)\) denote the set of all the upper triangular matrices with 1 along the main diagonal over the finite field \(\text{GF}(q)\) where \(q=p^e\) is a power of the prime \(p\). In a previous paper [J. Algebra 175, No. 1, 287-319 (1995; Zbl 0835.20052)], the author described some of the irreducible complex characters of the group \(U_n(q)\). In the paper under review, the author decomposes the regular character of \(U_n(q)\) in terms of certain characters of \(U_n(q)\).