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Die unipotenten Charaktere von \({}^ 2F_ 4(q^ 2)\). (The unipotent characters of \({}^ 2F_ 4(q^ 2))\). (German) Zbl 0721.20008
The author describes how to construct with the help of a computer (and he did) the classical irreducible characters and the Green functions of the Ree-groups \(G=^ 2F_ 4(q^ 2)\). The way is as follows. Reduction of the \({\mathbb{Z}}\)-lattice of characters obtained by induction of the irreducible characters of the two maximal parabolic subgroups, the maximal subgroups \({}^ 2B_ 2(q^ 2)\wr C_ 2\), \(B_ 2(q^ 2):2\) and \(SU_ 3(q^ 2):2\) yields all characters apart from the unipotent ones and the Deligne-Lusztig characters of two maximal tori. At this stage already 9 of the 11 Green functions are known.
The unipotent characters and the two remaining Green functions are then essentially computed using the degrees of the irreducible characters of G (which are known), properties of the Deligne-Lusztig characters and the orthogonality relations for Green functions. A table contains all the values of the 21 unipotent characters. The distribution of characters into blocks for all primes enables the author to confirm Brauer’s height conjecture, the conjecture on the number of irreducible characters in a given block and the Alperin-Mckay conjecture.
Reviewer: W.Willems (Essen)

20C33 Representations of finite groups of Lie type
20C15 Ordinary representations and characters
20C20 Modular representations and characters
20C40 Computational methods (representations of groups) (MSC2010)
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