4 problems

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

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…