12 problems

Let $W$ be a Coxeter group with $r$ conjugacy classes of simple reflections, and identify weight functions on $W$ with points of $V=\mathbb{R}^{r}$ having integer coordinates, call…

Cellularity conjecture. The Kazhdan–Lusztig basis of ${\mathcal H}_n$ is a cellular basis in the sense of Graham–Lehrer.

Fix a weighting $(s_1,s_2)\in \mathbb{Z}^2$ and set … Consider Geck's cellular Kazhdan–Lusztig-type basis of the type $B$ Hecke algebra and the graded cellular Murphy-type basis co…

Cyclic-cellularity conjecture. If $A$ is cyclic cellular, then so is $\mathcal{H}^{\mathbf{C}}_n(A)$.

Cellularity conjecture. The elements

Consider webs and resolve them according to the procedure explained in the source. Resolved-web cellularity conjecture. There is an ordering of the web resolutions such that the re…

Let $K_S$ be the algebra constructed from the chosen web and foam data, and suppose choices are made as in the method for obtaining a homogeneous basis of $K_S$. Graded cellular ba…

Let $R$ be a field, let $n$ be a positive integer, and let $W({\rm I}_2^n)$ be the corresponding dihedral group. The characteristic of $R$ is assumed not to divide $n$. Cellularity…

The algebras under discussion are cyclotomic Khovanov–Lauda–Rouquier algebras of type $A$, denoted $E^{\Lambda}_\alpha$, and a graded cellular basis is parametrised by pairs of bit…

Specht-module character conjecture. For all $n\in\mathbb N$ and all $\lambda\in\operatorname{Bip}(n)$,

Graham–Lehrer cellularity conjecture. The quadruple $((\operatorname{Bip}(n),\dominance_r),{\mathcal{S}}{\mathcal{B}}{\mathcal{T}},C^{\scriptscriptstyle{\leqslant}},*)$ is a cell d…

Let $\mathcal H$ be the Hecke algebra in the paper, let $\Lambda$ index its modules, and for each $\lambda\in\Lambda$ suppose that a $W$-graph affords an $\mathcal H$-module…