8 problems

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…

Let $S_N^+$ be the quantum permutation group and let $\mathcal A(S_N^+)$ be its Hopf $\ast$-algebra. A representation $\pi:\mathcal A(S_N^+)\to B$ is inner faithful when its kernel…

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

Stationary small-model conjecture. Under suitable assumptions,

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…