5 problems

Type-D family conjecture. The following assignments define standard homomorphisms:

Type-A twelve-period homomorphism conjecture. Define

Interval-family homomorphism conjecture. The assignments

A2 classification conjecture. Up to diagram automorphisms, either $M=A_{3m-1}$ for some $m\ge1$ and $\Phi=\Phi_{m,J}$ with $J\subset[1,m-1]$ as in Theorem, or $M=E_6$ and…

Dihedral injectivity criterion. Both induced maps $\overline\Phi$ and $\overline\Phi_\star$ are injective if and only if either both $\Phi$ and $\Phi$ are self-orthogonal, or $K$ s…