Semisimplicity of Hecke and (walled) Brauer algebras

We show how to use Jantzen’s sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of ${\mathbf{\text{U}}}_q$-tilting modules (for any field $\mathbb{K}$ and any parameter $q\in \mathbb{K}-\{0,-1\}$). As an application, we recover the semisimplicity criteria for the Hecke algebras of types $\mathbf{\text{A}}$ and $\mathbf{\text{B}}$, the walled Brauer algebras and the Brauer algebras from our more general approach.