I basically understand the rules of how to draw a Dynkin diagram but I couldn't find any rule for when I have to split edges like for the second last root of the $D_n$ diagram. Would be nice if somebody could give me an explanation.
2026-03-25 11:13:35.1774437215
Why is there a split in the second last root of the Dn Dynkin diagram?
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The Dynkin diagram of a root system $D_n$ represents a set of $n$ vectors in Euclidean space. Any two roots not joined by an edge are perpendicular. Any two roots joined by a single edge have angle $2\pi/3$. So, in $D_n, n\ge 4$, there is a certain root making angle $2\pi/3$ with each of three other roots, and the three other roots are all mutually perpendicular. Of course this does not fit in $\mathbb R^3$, but in some space of high enough dimension.