Classifying Nichols algebras over classical Weyl groups

In this article, we show that conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of $\mathit{\text{type}}\mathit{\text{D}}$. Consequently, we obtain that Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl groups ${\mathbb{W}}_n$ ($n\ge 5$) are infinite dimensional.