7 problems

For each $m\in\mathbb{N}$, let $\chi_m$ denote the algebra map defined in the paper. Chi-map isomorphism conjecture. The map $\chi_m$ is an isomorphism of algebras for all…

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…

Heisenberg categorification isomorphism conjecture. The injective algebra homomorphism $\mathbf{F}$ is an isomorphism.

Let $q$ be a parameter that is not a root of unity, let $\mathcal{H}(q)$ be the corresponding Heisenberg category, and let $\mathbf{F}$ be the functor from the Heisenberg algebra c…

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 $c_k$…

Endomorphism-algebra factorization conjecture. This natural map is an isomorphism. The claim says that, after adjoining closed diagrams from the identity endomorphism algebra, all…

Injectivity conjecture. The natural map is injective. This conjecture identifies the explicitly presented algebra $H_i^n$ with a subalgebra of the endomorphism algebra; the source…