13 problems

Racah algebra quotient conjecture. The centraliser for $sl_2$ is a quotient of $R(3)$.

Let $U(l/k)$ be the unitary supergroup, let $C_n(U(l/k))$ be its centralizer algebra, and let $T_{l/k}$ be the representation of $S_n$ under which this algebra is considered. For c…

Let $R$ be an arbitrary field or principal integral domain, let $c\in M_n(R)$, and let $d\in M_m(R)$. Write $S_n(c,R)$ and $S_m(d,R)$ for the associated centralizer matrix algebras…

Let $I^{>n}\subset U'_{-q^2}(\mathfrak{so}_{m})$ be the two-sided ideal generated by $\mathsf{x}_i^{(n+1)}$ for $i=1,\ldots,m-1$, and set … Let the Wenzl homomorphism be the surjec…

Affine Yangian centralizer decomposition conjecture. The centralizer $C(U(\widehat{\mathfrak{gl}}(m+n)),U(\widehat{\mathfrak{gl}}(n)))$ is isomorphic to the tensor product of the c…

Let $U(\mathfrak{sl}_2)$ act diagonally on the tensor product of any three irreducible representations, and let the centralizer be the algebra of endomorphisms commuting with this…

Let $A_{(\a4cH,\a4b4)}(\a4cH,\a4b4)$ denote the diagram-algebra deformation associated with the hyperoctahedral group, and let $A_{(\a4cH,\a4b4)}(\a4cH,\a4b4)(\infty)$ be its induc…

Let $j_1,j_2,j_3$ be representation labels and let $\mathcal{J}(j_1,j_2,j_3)$ be the set of admissible intermediate labels. For each $k\in\mathcal{J}(j_1,j_2,j_3)$, let…

Let $j_1,j_2,j_3$ be representation labels, let $AW(3)$ be the centrally extended Askey–Wilson algebra, and let $\mathcal{C}_{j_1,j_2,j_3}$ be the centralizer under consideration.…

Let $b1\in\mathbb{C}\setminus\mathbb{Q}$, let $H_n(\alpha)$ be the cubic Hecke algebra through which the braid-group representation factors, and let $r_2$ and $r_3$ be the relation…

Fix $b1 enewcommand$?

Let $\mathcal{W}'_{\mathfrak{q},N}$ be the associative algebra in the XXZ representation generated by $W\!B^{\alpha}_j$, with $1\leq j\leq N-2p+2$ and $\alpha\in\{0,\pm\}$, togethe…

Let the Gaussian representations be the braid-group representations studied by Rowell and Wang in the context of quantum computing, and let the centralizer algebras of quantum grou…