  We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over
classical Weyl groups $A \rtimes \mathbb S_n$ supported by $\mathbb S_n$ are
infinite dimensional, except in three cases. We give necessary and sufficient
conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl
groups $A \rtimes \mathbb S_n$ supported by $A$ to be finite dimensional.
