The mod p reduction of Weyl groups and their polynomial invariants

Question

Let $C$ be an $n\times n$ Cartan matrix, then the Weyl group $W\subset GL(n,Z)$. Let $W_p\subset GL(n,Z_p)$ be the mod p reduction of $W$. I want to know whether there are known work on the structure of the group $W_p$ and its polynomial invariants. I'm especially interested in the affine and indefinite cases. Advices and references are welcome.