A <root string> through $\beta$ in the $\alpha$ direction is the uninterrupted sequence $\beta-p\alpha,\ldots,\beta+q\alpha$ of roots, with $p-q=\langle\beta,\alpha^\vee\rangle$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 4 / a / iii / Solution

{wiki}

For roots $\alpha$ and $\beta$, the roots of the form $\beta+n\alpha$ form an unbroken string $\beta-p\alpha,\ldots,\beta+q\alpha$, and $p-q=\langle\beta,\alpha^\vee\rangle$.


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 Incoming links: Root string