Complete the classification of Nichols algebras over classical Weyl groups W(B_n) and W(D_n)

Complete the classification of Nichols algebras over the classical Weyl groups W(B_n) and W(D_n) by determining precisely, for each conjugacy class O and each irreducible representation ρ of the relevant centralizer, whether the associated Nichols algebra B(O,ρ) is finite dimensional.

Background

Prior work established many infinite-dimensionality results for Nichols algebras over symmetric groups and made progress for classical Weyl groups, but did not cover all cases. The authors emphasize that, despite advances, the classification over W(B_n) and W(D_n) had remained incomplete.

This paper advances the program by proving that conjugacy classes of W(B_n) and W(D_n) are of type D, implying infinite dimensionality for large families of Yetter-Drinfeld modules; however, the introduction explicitly notes the classification was not complete at the outset, framing the broader unresolved classification task.