14 problems

Let $U_q(\mathfrak{su}_2)$ act diagonally on the tensor product of three spin representations. The centralizer quotient conjecture. In general, the centralizer of this diagonal act…

Generator conjectures. The element $X^{\mu}_N$ generates $I^{\mu}_N$; the element $Y^{\mu}_N$ generates $I^{\mu}_N$; and

The universal-enveloping-algebra expression conjecture. For every $n$,

Hu's generalized surjectivity conjecture. The natural map $\psi'_{f,K}$ is surjective. The paper states that this conjecture implies the preceding algebraically closed-field conjec…

Hu's surjectivity conjecture. The map $\psi_{f,K}$ is surjective. This conjecture asks for the symplectic double-centralizer property on the quotient by the $f$-th Brauer ideal; it…

Let $\xi$ be a primitive $4m$th root of $1$, and let the $m$th twisted Lawrence–Krammer–Bigelow representation be the representation referred to below. Schur–Weyl duality conjectur…

Let $Q$ be a Dynkin quiver of finite type $E_n$. The functor $\mathcal{F}_Q^{(1)}$ is determined by $(U_q'(E_n^{(1)}),\phi_Q^{-1})$. KKK Schur–Weyl duality conjecture. The functor…

Mirabolic Schur–Weyl decomposition. The decomposition of $\mathrm{MT}_\mathbf{v}(2,d)$ as a bimodule for $MU_\mathbf{v}(2,d)$ and $R_d$ should be

Let $E[AS_m]$ be the group algebra of the affine symmetric group, let $\chi:E[AS_m]\to\operatorname{End}_{\operatorname{Sym}(\underline{x})}(R^m_n)$ be the specialization at $q=1$,…

Let $\mathcal{C}_Q$ be the smallest abelian full subcategory of $\mathcal{C}_{\mathrm{int}}$ satisfying the stated closure and generation conditions, and let … be the exact tensor…

Olshanski's entropy conjecture. For any $c>0$ with $c\neq 1$, there exists a positive number $H_c$ such that, for every $\varepsilon>0$,

Let $\mathbb F$ be any field, and let affine quantum Schur–Weyl reciprocity mean the mutual centralizer property for the affine Hecke and affine quantum Schur algebra actions on th…

Let $n$ and $r$ be as in the affine quantum Schur–Weyl construction, let ${\boldsymbol{\mathcal H}_{\!\vartriangle\!}(r)}$ and…

Let $f$ be an integer with $1\leq f\leq [n/2]$, let $K$ be an infinite field, let $V$ be the natural symplectic $K$-vector space, and let $\mathfrak{B}_n^{(f)}$ denote the relevant…