The EZ submodule conjecture

Let $Z_{p,m}$ and $Z_{p,m}'$ be the submodules defined above, and let $E_1$ be the first member of the corresponding filtration of submodules. EZ submodule conjecture. With the notation as above, we have

$$Z_{p,m}'=Z_{p,m}\cap E_1.$$

This is the first of two conjectures concerning the submodule structure of the polynomial representation, and the paper notes that it would follow from the stronger lattice-generation conjecture stated next.