Decomposition matrices for exceptional groups at d=4

We determine the decomposition matrices of unipotent $\ell$-blocks of defect $Φ_4^2$ for exceptional groups of Lie type up to a few unknowns. For this we employ the new cohomological methods of the first author, together with properties of generalized Gelfand-Graev characters which were recently shown to hold whenever the underlying characteristic is good.

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