2 problems

Proposed colored-face model. The ideal $SI'_{n,r}$ is stable under ${\mathbb{Z}}_r\wr{\mathfrak S}_n$, and there is a module isomorphism

Sagan–Swanson's conjecture. The set of monomials ${\mathcal{A}}_{n,r}$ descends to a vector space basis of $SR_{n,r}$.