4 problems

Uniqueness conjecture. The embeddings $H_N^+\subset S_{2N}^+$ and $\bar{O}_N\subset S_{2^N}^+$ are the unique embeddings which can make a quizzy quantum group a quantum permutation…

Let $G\subset S_N^+$ be quasi-transitive, with all orbits of size $K$, and let … be its universal quasi-flat model. The uniformity conjecture. If $G$ additionally satisfies a suita…

Let $G\subset S_N^+$ be quasi-transitive, with all orbits of size $K$, and write $\Gamma=\widehat{G}$. Let $X_G$ be the universal quasi-flat model space and let … be the correspond…

Let $G\subset S_N^+$ be a quantum permutation group whose orbits have the same size $K$, and let … be its universal quasi-flat model, whose standard coordinates are represented by…