6 problems

Suppose $c_0=j/k$ with $k$ and $j$ relatively prime positive integers, and $2\leq k\leq n$. Let $\mathbf{C}[\mathfrak{h}]$ be the polynomial representation, and let…

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 not…

Let $B_0$ be the principal block, let $\Lambda_\lambda$ and $\bar{\Gamma}_\lambda$ be the poset and graph subsets defined by the algorithm, and let $d(\mu,\lambda)$ be the grading…

Let $W=B_{2n}=G(2,1,2n)$ and let the parameter $c=1/(2n)$ be constant. Write $\Delta_i$ and $\Delta_{2n-i}$ for the standard-module sums specified in the preceding theorem, and let…

Gorenstein and palindromicity conjecture. If $\tau$ is trivial, then $M_c(S_n,\mathfrak{h},\tau)/J_c(S_n,\mathfrak{h},\tau)$ is Gorenstein for all $n$, both when $c\in\mathbf{F}_p$…

Degree-sum conjecture. The sum of the degrees in a minimal generating set of $J_{c+1}(S_n,\mathfrak{h},\tau)$ is exactly $n!$ greater than the corresponding sum for…