10 problems

Wheeling conjecture. Wheeling intertwines the two products on Chinese characters; more precisely,

Wheels conjecture.

Let $\psi_0$ be the surjective map constructed from the algebra of diagrammatic generators to the relevant algebra of endomorphisms, with proposed free generators…

Let $q=e^{\frac{2\pi i}{r}}$ with an even integer $r\geq 4$, let $\bar{U}$ be the restricted quantum group of $\mathfrak{sl}_2$, and let $X$ be the fundamental simple module of dim…

Injectivity conjecture. The map $\eta$ is injective.

Let a diagrammatic category be a monoidal category whose morphism spaces are depicted by string diagrams, with $0$-composition given by horizontal concatenation and $1$-composition…

Let $B$ be the graded algebra under consideration, let $B_\psi=B/\langle b-\psi(b)\mid b\in B\rangle$, and let $C$ be the graded vector space with basis $v_d$ for…

Let $\mathsf{D}_{{\mathfrak S}(n)}$ be the diagrammatic representation-theoretic object associated with the symmetric group ${\mathfrak S}(n)$, and let $\mathsf{P}^{(n)}$ be its id…

Let $I$ be the vertex set of the Dynkin diagram. For $i\in I$ and $k\in\mathbb{N}$, let $c_k^i$ be a clockwise circle labeled $i$ containing exactly $k$ hollow dots, and let $c_k$…

Let $lambda\rightarrow\ru(n,d)$ be arbitrary, and let $mu\rightarrow\ru(n,d)$ be obtained from $lambda$ by moving all zero entries to the end while preserving the relative order of…