11 problems

Easy quantum group conjecture. Every quantum group $G$ with $S_N^+\subset G\subset U_N^+$ must be easy.

The relevant standard tori of an easy compact quantum group $G$ are considered in the generalized standard torus setting. The Fourier tori are the standard tori associated with the…

Free easy quantum group factor conjecture. The associated von Neumann algebra $L^\infty(G)$ is a factor.

First-column-space conjecture. The map

Fourier liberation conjecture. Every easy quantum group satisfies FL, SL, and GT.

Let $G_N$ be a closed quantum subgroup of $U_N^+$, and let $S_N^+$ be the free symmetric quantum group. Denote by $G_N'$ the easy envelope of $G_N$, and write $\{\,,\}$ for the eas…

Let $O_N$, $O_N^*$ and $O_N^+$ denote the orthogonal, half-liberated orthogonal and free orthogonal quantum groups, respectively. Let $B_N$, $B_N^\circ$ and $B_N^+$ denote the corr…

Banica's restriction conjecture. The axioms should substantially restrict the list of known examples of such quantum groups. The classification problem for these intermediate liber…

An easy geometry consists of the category of partitions $D$, its associated quantum group $G$, its associated discrete group or noncommutative torus $T$, and the corresponding sphe…

Let $\mathbb{G}$ be a free unitary easy quantum group without any non-trivial one-dimensional representation. Let $\mathcal{C}^{\circ,\bullet}$ be its category of noncrossing color…

Let $\mathbb{G}$ be a free unitary easy quantum group. A free fusion semiring is obtained from a set $S$ with an involution and a binary law by taking the free monoid $R(S)$, with…