6 problems

Let $G$ be a split reductive group with Weyl group $W$, root lattice $\Phi$, and $V=\mathbf{Z}\Phi\otimes_{\mathbf{Z}}\mathbf{Q}$. Let $\mathit{Br}_W^+$ denote the positive braid m…

Let $G$ be a complex, connected, reductive algebraic group, let $B_+$ and $B_-$ be opposed Borel subgroups, and let $U_+$ and $U_-$ be their unipotent radicals. Let…

Let $\mathcal G$ be one of $G$, $\mathfrak g$, or $\mathfrak g^*$, and let $H^{\blacktriangle}(\mathcal G)$ and $X^{\vartriangle}(\mathcal G)$ denote the corresponding pieces, with…

Let $G$ be a connected reductive group over an algebraically closed field. For each $\blacktriangle\in D_G/G$ and $\blacktriangle\in D_G$, let $H^{\blacktriangle}$ and…

Geck–Malle special-piece conjecture. The algorithm in this form can be used to compute the number of $\mathbb{F}_q$-points in a special piece of the unipotent variety.

Let $P$ be a special piece in the unipotent variety of a reductive algebraic group. Normality conjecture for special pieces. Every special piece $P$ is normal. This is a necessary…