A third look at weight diagrams

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Structure of Chevalley groups: The proof from the book (2007, methodology): “Both the form [66, 53] and the signs [ 68 , 8] of these equations can be recovered directly from the weight diagram of the corresponding representation.”
K1 of Chevalley groups are nilpotent (2003, background): “…α (a), g] with one general matrix g ∈ G for the classical groups in vector representations, [11], [12], [25], [16], or for the groups of types E 6 or E 7 in micro-weight representations, [25], [27], [26], would immediately recognise, that writing a similar formula for our problem was not an option.”
Bak's work on the K-theory of rings (2009, background): “On a different slope, let us refer to the papers [163]—[167] by the second-named author and his students where one can find a detailed comparison of various proofs of these results for commutative rings, and their generalisations to exceptional groups.”
Structure of Hyperbolic Unitary Groups I: Elementary Subgroups (2000, methodology): “Another approach to prove this result, based on Stepanov’s idea of decomposition of unipotents, was proposed in [56, 80, 82 , 84, 85].”