Decomposition of Cartan Matrix and conjectures on Brauer character degrees

Zeng Jiwen

Let $G$ be a finite group and $N$ be a normal subgroup of $G$. Let $J=J(F[N])$ denote the Jacboson radical of $F[N]$ and $I=\mathrm{Ann}(J)=\{\alpha \in F[G]|J\alpha =0\}$. We have another algebr…