12 problems

Let $H$ be a Hecke algebra of type A, and let $L_1,\ldots,L_n$ denote its Jucys–Murphy elements. A polynomial in these elements is symmetric if it is invariant under permutations o…

Conjecture 3. The elements $C_q$, $T_1^n$, $T_2^n$ and $C^{(n)}(I)$ generate the center of $U'_q({\rm iso}_2)$.

Conjecture 2. The central elements of [9] and of Theorem 4 generate the center of $U'_q({\rm so}_m)$.

Conjecture 1. The elements $C_q$ and $C^{(n)}(I_j)$, $j=1,2,3$, generate the center of $U'_q({\rm so}_3)$.

Center conjecture. The center of $B_n(q,q^{2a})$ is

Jung and Kim's conjecture. For every $\delta \in \mathbb{C}$, the center of the walled Brauer algebra $B_{r,s}(\delta)$ is generated by the supersymmetric polynomials in the Jucys–…

The center and finite generation conjecture. We have

Let $Alt[X]$ be the free alternative algebra, let $Z=Z(Alt[X])$ denote its center, and regard the degree of an element as its total degree in the free generators. Filippov's conjec…

Let $k$ be an uncountable algebraically closed field of characteristic zero, and let $A$ be an affine noetherian domain over $k$. Write $Z(A)$ for the centre of $A$. An algebra is…

Assume ${\mathfrak{A}}={\mathfrak{A}}_\pi$, so that $U=U_\pi(\chi,\pi)$. Let $\omega:{\mathfrak{A}}\to\mathbb{K}^\times$ be a $\mathbb{Z}$-module homomorphism. For…

Cho–Hong–Lau's center conjecture. The elements $C_1$ and $C_2$ generate the center of $R(a,b,c,d)$. This is a structural conjecture about the degree-two central elements of the fam…

Center conjecture. The image of the canonical map