6 problems

Let ${\mathcal A}$ be a complex hyperplane arrangement, let $A=H^*(X({\mathcal A}),\Bbbk)$ be its Orlik-Solomon algebra over a field of characteristic $0$, and let $E$ be the exter…

Let $\mathcal{A}$ be a hyperplane arrangement, let $e_p(\mathcal{A})$ denote the relevant exponent of its algebraic monodromy, and let $\beta_p(\mathcal{A})$ denote the dimension o…

Lehrer–Solomon conjecture. There should be a $\mathbb{C}W$-module isomorphism

Let $W$ be a finite Coxeter group of rank $n$, let $\mathcal R$ be a set of representatives of its conjugacy classes, and let $C_W(w)$ be the centralizer of $w$. Let $\rho_W$ be th…

Let $W$ be a finite Coxeter group, let $V$ be its reflection representation, and let $M$ be the complement of the reflecting hyperplanes. For each $p$, write $omega_W^p$ for the ch…

Orlik–Solomon and descent-algebra character conjecture. For each $c\in\mathcal C$, there is a linear character $\varphi_c$ of $Z_W(c)$ such that, for every $\lambda\in\Lambda$, the…