Character table and blocks of finite simple triality groups ³𝐷₄(𝑞)

Deriziotis, D. I.; Michler, G. O.

doi:10.1090/S0002-9947-1987-0896007-9

Character table and blocks of finite simple triality groups $^ 3D_ 4(q)$
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by D. I. Deriziotis and G. O. Michler PDF

Trans. Amer. Math. Soc. 303 (1987), 39-70 Request permission

Abstract:

Based on recent work of Spaltenstein [14] and the Deligne-Lusztig theory of irreducible characters of finite groups of Lie type, in this paper the character table of the finite simple groups ${}^3{D_4}(q)$ is given. As an application we obtain a classification of the irreducible characters of ${}^3{D_4}(q)$ into $r$-blocks for all primes $r > 0$. This enables us to verify Brauer’s height zero conjecture, his conjecture on the bound of irreducible characters belonging to a give block, and the Alperin-McKay conjecture for the simple triality groups ${}^3{D_4}(q)$. It also follows that for every prime $r$ there are blocks of defect zero in ${}^3{D_4}(q)$.

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