Extend the radical-filtration description to arbitrary Weyl modules

Prove that the radical filtration of every Weyl module over Lusztig’s quantum group satisfies the stated Kazhdan–Lusztig conditions, including semisimplicity of its layers and the prescribed multiplicities.

Background

The paper assumes the existence of filtrations on Weyl modules whose layers are semisimple and whose multiplicities are governed by affine Kazhdan–Lusztig polynomials. A filtration with these properties is known in some types and for affine dot-regular weights. The authors identify the extension of the radical-filtration description to arbitrary weights as unresolved.

References

If $\lambda$ is an affine dot-regular weight then the filtration of is simply the radical filtration; it is expected, but not known (as far as we are aware), that this holds for arbitrary $\lambda$.

— Weights of KZ motives and quantum groups  (2610.26774 - Belkale et al., 19 Oct 2026) in Section 2, subsection “Filtrations on Weyl modules”

We do not know if this holds for all Weyl modules.

— Weights of KZ motives and quantum groups  (2610.26774 - Belkale et al., 19 Oct 2026) in Remark 2.14, Section 2, subsection “Filtrations on Weyl modules”