2 problems

Let $k$ be a field of characteristic not equal to $2$, and let $B\operatorname{Spin}_n$ denote the classifying space of the spin group $\operatorname{Spin}_n$ over $k$. A variety i…

Let $E_8$ be the compact exceptional Lie group, and let $\sigma'$ be the involution induced by an element of $Spin(8)\subset F_4\subset E_6\subset E_7\subset E_8$. For a subgroup…