63 problems

Let $W$ be a complex reflection group, let ${\mathcal{C}}$ be its Calogero–Moser parameter space, and let $\kappa:{\mathcal{C}}\rightarrow{\mathcal{K}}$ be the parameter correspond…

Let $W$ be a complex reflection group, let ${\mathcal{C}}$ be its parameter space, and let $\kappa:{\mathcal{C}}\rightarrow{\mathcal{K}}$ identify Calogero–Moser parameters with He…

Let $W$ be a complex reflection group, let $B(W)$ be its braid group, let $\mathcal{H}(W)$ be its generic Hecke algebra, and let $\tau$ be a canonical symmetrising trace on…

Let $W\subset GL(V)$ be a complex reflection group, let $R(W)$ be its associated Laurent polynomial ring, and let $\mathcal{H}(W)$ be the associated generic Hecke algebra over…

Let $W$ be a complex reflection group, let $R(W)$ be its ring of definition, and let $\mathcal{H}(W)$ be its generic Hecke algebra. Let $B(W)$ be the braid group, let…

Let $W$ be a well-generated finite complex reflection group, and let $T$ and $T'$ be reflection factorizations of a Coxeter element of $W$. Two factorizations are said to have the…

Conjecture. The groups $B$ and $P$ are linear and satisfy all the properties enumerated in that theorem whenever $W$ is an irreducible complex reflection group.

Bessis's modified-action CSP conjecture. The triple

The hsop existence conjecture. If $p\equiv 1\pmod h$, then $S$ contains an hsop $\mathbf{\Theta}$ carrying $V^*(-p)$; if $p\equiv -1\pmod h$, then $S$ contains an hsop…

Let $W$ be a well-generated finite complex reflection group with degrees $d_1,\dots,d_n$ and Coxeter number $h$, let $d$ be a regular degree, let $W'$ be the centralizer of a $d$-r…

Let ${\bf w}$ be an $F$-root of ${\boldsymbol\pi}$, put $w=\beta({\bf w})$, and let $C_W(wF)$ be the centralizer of the corresponding regular element of $WF$. Let $B(w)$ be the bra…

Let $B$ be the braid group associated with a well-generated complex reflection group, let $\mathcal{R}$ be its set of braid reflections, and let $\delta$ be the braid-group analogu…

The $G_{34}$ braid-group conjecture. The braid group associated with $G_{34}$ admits the presentation

The $G_{33}$ braid-group conjecture. The braid group associated with $G_{33}$ admits the presentation

The $G_{31}$ braid-group conjecture. The braid group associated with $G_{31}$ admits the presentation

The $G_{29}$ braid-group conjecture. The braid group associated with $G_{29}$ admits the presentation

Let $A=\mathbb{Z}[x,x^{-1}]$, let $R$ be a commutative local $A$-algebra, and let $F$ be its residue field. Let ${\mathcal H}$ be the Hecke algebra of a finite complex reflection g…

Let $W$ be a finite complex reflection group, let $W'$ be a parabolic subgroup, and let ${\mathcal H}(W)$ be the associated Hecke algebra. A canonical symmetrizing form on…

Let $W$ be a finite complex reflection group, let $W'$ be a parabolic subgroup of $W$, and let ${\mathcal H}(W)$ and ${\mathcal H}(W')$ be their Hecke algebras over…

Bessis–Digne–Michel's centralizer conjecture. The natural morphism

Generalised Trinh–Xue conjecture. The intersection of the $\Phi$- and $\Phi'$-Harish-Chandra series

Wedge-of-spheres conjecture.

Let $m$ be even, let $\frac{m}{p}$ be odd, and set $k=\mathbb{Q}(\sqrt[m]{1})$. Let $\underline{\overline{H}}_{\underline{c}}(\mu(G(m,p,n)))$ and $\overline H_c(G(m,p,n))$ be the t…

Let $G(m,p,n)$ be a complex reflection group, let $J_1$ and $J_{-\mathbf i}$ be the character-twisting maps considered in the paper, and let $\chi$ be a character of $G(m,p,n)$. Tw…

Super Artin basis conjecture. The set ${\mathcal S}{\mathcal A}_{m,n}$ is a basis for $\operatorname{SRG}_{m,n}$.