2 problems

Let $\bG$ be a reductive algebraic group over a field of characteristic $p$, let $F$ be a Frobenius endomorphism, and let $\chi\in\operatorname{Irr}(\bG^F)$. Assume that $p$ is a g…

Let $n$ be a positive integer, let $\mu=(\mu_1,\mu_2,\dots)$ be a partition of $n$, and let $\tau$ be a partition of $n$. For triples of partitions define … where…