= Cn Dynkin diagrams
{c}
{title2=$C_n,\quad C_n^{(1)}$}
For $n\ge2$, the finite <Dynkin diagram> has a chain of <short roots> $\alpha_1,\ldots,\alpha_{n-1}$ with single bonds, followed by a double bond to the <long root> $\alpha_n$, pointing toward $\alpha_{n-1}$. The <Extended Dynkin diagram> adds the long root $\alpha_0=-2\varepsilon_1$, doubly bonded to $\alpha_1$ with arrow toward $\alpha_1$. All other bonds remain. For $n=1$, the finite diagram is a single vertex; the affine diagram has two equal-length vertices joined by a double bond without an arrow, with <Cartan matrix> $\begin{pmatrix}2&-2\\-2&2\end{pmatrix}$.
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