3 problems

Let $\Gamma$ be the Brauer tree of the principal $\Phi_h$-block. The characters $\chi_{m_\zeta}$ arise from the Frobenius eigenspaces in the rational $\ell$-adic cohomology, and th…

Let $\Gamma^\bullet$ denote the graph obtained from the Brauer tree of the principal $\ell$-block by removing the exceptional node and all edges incident to it. For each root of un…

Let $G$ be a finite reductive group whose principal $\ell$-block has cyclic defect, and let $h_0$ be the relevant order of the roots of unity occurring in the block. Let $q^\delta$…