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Meinolf Geck and Götz Pfeiffer,

Unipotent Characters of the Chevalley Groups D4(q), q odd.

Manuscripta Math. 76 (1992), 281-304.

Abstract.

Let q be an odd prime power and D4(q) be a finite Chevalley group with root system of type D4. In this paper we determine the values of the unipotent characters of D4(q), based on G.Lusztig's parametrization of characters and on the recent work of L.Lambe and B.Srinivasan on the Green functions for some classical groups. We emphazise the role of the computer algebra systems GAP and MAPLE for computations in the Weyl group and symbolic calculations with characters. The results will then be applied to answer some questions concerning the modular representation theory of D4(q). In particular, we show that the unique cuspidal unipotent character of D4(q) remains irreducible as l-modular Brauer character, for all primes l not dividing q.

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