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I have re-arranged slightly:
Re-ordered the references (in an entry on Dynkin diagrams a reference on application of Dynkin indices to mathematical physics should probably not precede references on the maths of Dynkin diagrams).
In fact, probably Dynkin index should be a separate entry altogether.
removed the empty “Proof” subsection: Proofs should not be subsections but proof environments (see at HowTo here). Also, there is no discernible theorem stated yet, so it seems out of place to announce a proof. Once you have a theorem statement and really go about writing the proof, just type \begin{proof}... \end{proof}
added a direct link from the text to your reference Myers, de Roo & Sorba 1979. That looks like a good reference, thanks for adding it. Maybe all you really mean to do here is to point the reader to there for more, which is worthwhile. For that a Remark environment seems appropriate, and so I have made one (here).
changed the broken pointer to “topological charge” to one to instanton number
A lot of the Dynkin index material is lifted from here. I agree it should go in its own entry, and linked to concepts like the index of the image of the restriction map $H^4(B G)\to H^4(B K)$, of the inclusion map $\pi_3(K)\to \pi_3(G)$ (both associated to a subgroup inclusion $K\hookrightarrow G$) and so on.
Thank you for the pointers. Yes, I used the Dynkin index entry in the SUSY encyclopedia (listed in references) as a starting point.
Is the index of the image of the restriction map above related to a faithful embedding, defined by some injective map $f$ of an algebra $\tilde{G}$ into $G$ via $\tilde{X}\rightarrow f(\tilde{X}) \in G$?
Would the restriction map of the inclusion map as shown above just be a deformation retraction from $G$ to $K$?
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