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Let $a,b$ be roots ($a\ne \pm b$) of a Lie algebra $g$ of type $X$, where $X$ can be classic or exceptional $(A,B,C,D,E,F,G)$. It is well known that the length of an $a$-string through $b$ is at most 4.

What are all types of $g$ such that:

1) $a+b$ is a root and $a+2b$ is not a root?

2) $a+2b$ is a root and $a+3b$ is not a root?

3) $a+3b$ is a root?

Thanks!

  • 0
    Could you please clarify what is meant by the term "scenery" (in particular, "biggest scenery")?2010-12-28
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    @Brad: I edited the text.2010-12-29

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