3 problems

Symmetric generation conjecture. The subspace $\omega^\perp\cap {\rm Sym}(S)$ is the subalgebra of the Norton algebra $EV$ generated by $E\hat x+E\hat y$.

Symmetric-subspace closure conjecture. We have

Let $\Gamma=(X,\mathcal R)$ be the bilinear forms graph, let $x,y\in X$ be adjacent vertices, and let $U=U(x,y)$ be the subspace defined earlier. Let $E=E_1$ be the primitive idemp…