8 problems

Let $\mathbb{G}=(W,\Lambda)$ be a $\mathbb{Z}_\ell$-reflection group with $(|W|,\ell)=1$, and let $T_a=\Lambda/\ell^a\Lambda$. For $b\ge a$, regard each…

Let $\mathbb{G}=(W\phi,\Lambda)$ be a simply connected $\mathbb{Z}_\ell$-spets and let $q\in\mathbb{Z}_\ell^\times$. Let $S$ be the Sylow $\ell$-subgroup of $(\mathbb{G},q)$, let…

Let $\mathbb{G}=(W,\Lambda)$ be a simply connected $\mathbb{Z}_\ell$-spets with $\ell>2$ and $(|W|,\ell)=1$. Let $T$ be the Sylow $\ell$-subgroup of $\mathbb{G}(q)$, let…

Let $\mathbb{G}=(W,\Lambda)$ be a simply connected $\mathbb{Z}_\ell$-spets such that $\ell>2$ is very good for $\mathbb{G}$ and coprime with $|W|$. Let $q\in1+\ell\mathbb{Z}_\ell$,…

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

Let $\mathbb{G}=(W\varphi^{-1},L)$ be as in the principal-block dimension conjecture, and suppose that $W$ is an $\ell'$-group, $\varphi$ is trivial, and $q\equiv1\pmod\ell$. Let…

Principal-block dimension conjecture.

Let ${\mathbb{G}}$ be a simply connected ${\mathbb{Z}}_\ell$-spets, let $\ell>2$ be very good for ${\mathbb{G}}$, and let $q$ be a power of a prime different from $\ell$. Let $B_0$…