Perfect Isometries Between Blocks of Complex Reflection Groups

Abstract

In this paper, we prove that, given any integers $d$, $e$, $r$ and $r^{\prime }$, and a prime $p$ not dividing $de$, any two blocks of the complex reflection groups $G(de,e,r)$ and $G(de,e,r^{\prime })$ with the same $p$-weight are perfectly isometric.