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By coincidence i stumbled over this page

http://www.fields.utoronto.ca/programs/scientific/11-12/exceptional/abstracts.html

, which was installed for a workshop on algebraic groups in 2012.

In the upper left you will see several Dynkin diagramms of Root Systems. Just under $F_4$ there is one named $H_3$, another one named $H_4$ and i think there is also $L_2$.

What are these and where can i found out more about them?

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  • $\begingroup$ Although it's relatively easy to answer, I think that this is a good question. Gro-Tsen asked a similar question a year later, at mathoverflow.net/questions/247718/… ; with no slight to that fine user, I'm not sure why it received such a different reception. $\endgroup$
    – LSpice
    Commented May 8, 2019 at 1:02

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It's actually $I_n$, not $L_2$ (the print is very small). These diagrams classify finite Coxeter groups ($I_n$ is the family of dihedral groups and $H_3$ and $H_4$ are automorphism groups of certain exceptional polytopes). The three that you mention aren't Weyl groups, so don't come from an algebraic group like the other ones do. More information on the wiki page: http://en.wikipedia.org/wiki/Coxeter_group#Properties

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  • $\begingroup$ Good to know its that easy, thanks. $\endgroup$
    – nxir
    Commented Apr 27, 2015 at 21:59

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