7 problems

Let $\mathcal Q_n$ be the quantum permutation group on $n$ points, containing the classical symmetric group $S_n$. Maximality conjecture. The symmetric group $S_n$ is maximal in th…

Let $S_N^+$ be the quantum permutation group, and let $X_N$ be the compact space of $N\times N$ matrices $P=(P_{ij})$ whose entries are rank-one projections in $M_N(\mathbb C)$ sat…

Homogeneous model-space conjecture. Under the stated strong uniformity assumption:

Stationary $K$-model conjecture. Under these assumptions, the following are equivalent:

$F_p$-monotonicity conjecture. For every $x\in U_N^N$ and every $p\geq2$,

Let $S_N^+$ be the quantum permutation group, let $X_N$ be the associated matrix-model space, and let … be the universal $N\times N$ flat matrix representation. Flat matrix represe…

Convergence conjecture. The maps $\Phi$ and $\Psi$ increase the volume and, after an infinite number of steps, respectively land in $K_N$ and $X_N$. This conjecture would imply con…