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Values of the unipotent characters of the Chevalley group of type $$F_ 4$$ at unipotent elements. (English) Zbl 0869.20005
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 N. Kawanaka [Invent. Math. 84, 575-616 (1986; Zbl 0596.20028)] and G. Lusztig [J. Algebra 104, 146-194 (1986; Zbl 0603.20037)].

##### MSC:
 20C33 Representations of finite groups of Lie type 20G05 Representation theory for linear algebraic groups
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