  We show how to use Jantzen's sum formula for Weyl modules to prove
semisimplicity criteria for endomorphism algebras of $\textbf{U}_q$-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 $\textbf{A}$ and $\textbf{B}$, the
walled Brauer algebras and the Brauer algebras from our more general approach.
