Values of the unipotent characters of the Chevalley group of type \(F_ 4\) at unipotent elements (Q1913552)

Let \(G\) be a Chevalley group over the finite field \(F_q\) of characteristic \(p\). The authors call the table consisting of the values at unipotent elements of the unipotent characters of \(G\) the unipotent character table of \(G\). The purpose of this paper is to form the unipotent character table of \(G\) of type \(F_4\) in the cases \(p=2\) or 3. If \(G\) has type \(F_4\) and \(p\geq 5\), the problem of completing the unipotent character table of \(G\) is reduced to the determination of the values of one almost character; this was settled independently by \textit{N. Kawanaka} [Invent. Math. 84, 575-616 (1986; Zbl 0596.20028)] and \textit{G. Lusztig} [J. Algebra 104, 146-194 (1986; Zbl 0603.20037)].