# 2025-02-03-19-35-05


:::{.definition}
We say a Coxeter system $(W, S)$ is **irreducible** if the Coxeter graph $\Gamma_W$ is connected.
:::

:::{.proposition}
The center $Z(W)$ of an irreducible, infinite Coxeter system $(W, S)$ is trivial.

The proof of this is in \cite[Prop.\, 2.5]{qiIrreducibleInfiniteNonaffine2006}.
:::