8 problems

Let $W$ be an irreducible complex reflection group that need not be well-generated. The proposed general construction associates a dual braid monoid to a regular degree and maps it…

Type-D family conjecture. The following assignments define standard homomorphisms:

Type-A twelve-period homomorphism conjecture. Define

Interval-family homomorphism conjecture. The assignments

B2 classification conjecture. Homomorphisms from any of those three stated families exhaust, up to diagram automorphisms, all fully supported standard homomorphisms from…

A2 classification conjecture. Up to diagram automorphisms, either $M=A_{3m-1}$ for some $m\ge1$ and $\Phi=\Phi_{m,J}$ with $J\subset[1,m-1]$ as in Theorem, or $M=E_6$ and…

Dihedral injectivity criterion. Both induced maps $\overline\Phi$ and $\overline\Phi_\star$ are injective if and only if either both $\Phi$ and $\Phi$ are self-orthogonal, or $K$ s…

Let $W$ be a finite well-generated complex reflection group, and let its dual braid monoid be defined using the noncrossing partition lattice. Consider the simplicial complex whose…