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January 27, 2012

G2 and Spin(8) Triality

Oscar Chacaltana, Yuji Tachikawa and I are deep in the weeds of nilpotent orbits. One of the things we had to study were the nilpotent orbits of 𝔤 2\mathfrak{g}_2, and how they sit in 𝔰𝔬(8)\mathfrak{so}(8). Understanding the answer involves an explicit description of Spin(8)Spin(8) triality, which I thought was kinda cute. Few people will care about the nilpotent orbits, but the bit about triality and G 2G_2 might be of some independent interest. So here it is.

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Posted by distler at 2:09 PM | Permalink | Followups (12)