2-blocks and 2-modular characters of the Chevalley groups 𝐺₂(𝑞)

Hiss, Gerhard; Shamash, Josephine

doi:10.1090/S0025-5718-1992-1134731-9

$2$-blocks and $2$-modular characters of the Chevalley groups $G_ 2(q)$
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by Gerhard Hiss and Josephine Shamash PDF

Math. Comp. 59 (1992), 645-672 Request permission

Abstract:

We first determine the distribution of the ordinary irreducible characters of the exceptional Chevalley group ${G_2}(q)$, q odd, into 2-blocks. This is done by using the method of central characters. Then all but two of the irreducible 2-modular characters are determined. The results are given in the form of decomposition matrices. The methods here involve concepts from modular representation theory and symbolic computations with the computer algebra system MAPLE. As a corollary, the smallest degree of a faithful representation of ${G_2}(q)$, q odd, over a field of characteristic 2 is obtained.

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