Centrality of root-vector pth powers in type C

Prove that the pth powers of all positive and negative Lyndon root vectors in the modular Yangian of a classical Lie algebra of type C are central.

Background

The paper defines the restricted Yangian in characteristic p>3 by quotienting the modular Yangian by the ideal generated by the pth powers of positive and negative Lyndon root vectors together with specified central Cartan elements. For types A, B, and D, the centrality of the positive root powers is known and the centrality of the negative root powers follows from the anti-automorphism interchanging positive and negative generators.

For type C, however, the centrality of these root-vector pth powers is only identified as a conjecture from earlier work. Establishing this centrality would complete the corresponding centrality statement across all classical types and substantiate the proposed restricted-Yangian quotient in type C.

References

In types $A,B,D$, the positive root powers are central by Theorem~4.6, and the negative ones are central by the anti-automorphism $\tau$. In type $C$, their centrality is conjectured in Remark~4.7.

— Integral forms for Yangians of classical type  (2610.05988 - Chang et al., 5 Oct 2026) in Section 5, immediately before Lemma 5.2 (the paragraph introducing the restricted Yangian)