9 problems

Let $\hat {\cal B}_{m}^{\,u}$ be the diagram space with filtration quotients ${\cal G}_{f,o,e}^{\,}\,\hat {\cal B}_{m+2f}^{\,u}$, where $f,o,e$ are the filtration parameters. Vanis…

Let $\hat {\cal B}_{m}^{\,u}$ be the diagram space equipped with the filtration whose quotient at $(f,o,e)$ is ${\cal G}_{f,o,e}^{\,}\,\hat {\cal B}_{m}^{\,u}$. Let $T(m,u)$ be the…

Let … , let … and … such that … The conjecture proposes that these algebras are isomorphic for a suitable choice of parameter. The supplied text gives no proof or resolution.

Let $k$ be a positive integer, let $\mathcal{A}_{2k}^{\text{aff}}$ be the affine partition algebra, and let $z_l$ and $p_n$ denote the central elements introduced in the paper for…

Let $A(n)$ be the space defined by the two-dimensional topological theory, and let $\mathscr{A}^m(n)$ be the set of surface diagrams whose connected components satisfy the genus bo…

Let $\Theta$ be the coupled Young graph, let $\mathcal{P}(\Theta)$ be its pascalization, and let $A_{(\mathcal{C}_H,\delta)}(\infty)$ be the associated inductive limit algebra at t…

Let $\mathcal T$ be the free PRO under consideration, let $\mu$ be a representation of $\mathcal T$ of dimension $N$, and let $d$ denote the parameter appearing in the trace of the…

Let $m,n$ be natural numbers and fix a block ${\mathcal B}$ of atypicality $k$ in ${\mathcal F}(\operatorname{SOSP}(m|2n))$. Let $\mathbb{H}_k^\infty$ be the limiting graded diagra…

Barad's factorization conjecture. The determinant satisfies