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Unipotent characters of the Chevalley groups \(D_ 4(q)\), \(q\) odd. (English) Zbl 0813.20016
The authors determine (using the computer algebra systems GAP and MAPLE) the values of the unipotent characters of the Chevalley groups \(D_ 4(q)\) where \(q\) is an odd prime power. The work is based on G. Lusztig’s parametrization of characters [Characters of reductive groups over finite fields (Ann. Math. Stud. 107, 1984; Zbl 0556.20033)] of such groups and the work of B. Srinivasan on the Green functions for some classical groups. As an application to the modular representations of such groups the authors prove that the unique cuspidal unipotent character of \(D_ 4(q)\) remains irreducible as \(\ell\)-modular Brauer character for all primes \(\ell\) not dividing \(q\).

MSC:
20C33 Representations of finite groups of Lie type
20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
Software:
GAP; Maple
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References:
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