## January 27, 2012

### G_{2} 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 $\mathfrak{g}_2$, and how they sit in $\mathfrak{so}(8)$. Understanding the answer involves an explicit description of $Spin(8)$ triality, which I thought was kinda cute. Few people will care about the nilpotent orbits, but the bit about triality and $G_2$ might be of some independent interest. So here it is.