Compute Andersen filtrations for tensor products of simple modules

Develop a general method for computing the generalized Andersen filtration on Hom spaces associated with tensor products of simple modules over Lusztig quantum groups at roots of unity.

Background

The conjectures identify weight filtrations of KZ variations with filtrations arising from quantum-group representation theory. Computing these filtrations requires explicit knowledge of the generalized Andersen filtration on tensor products of simple modules. The paper provides such computations in the case of Fsl2F\mathfrak{sl}_2, but states that no general method is currently known.

References

While tensor products of tilting modules may be computed algorithmically, it is not known in general how to compute the (generalised) Andersen filtration for tensor products of simple modules.

— Weights of KZ motives and quantum groups  (2610.26774 - Belkale et al., 19 Oct 2026) in Introduction, subsection “Methods”

As far as we are aware, this conjecture is not known in general even for affine dot-regular $\lambda$ and $F{g} = F{sl}_m$, but it is easy for $F{sl}_2$.

— Weights of KZ motives and quantum groups  (2610.26774 - Belkale et al., 19 Oct 2026) in Section 2, subsection “The Andersen filtration and Kazhdan–Lusztig polynomials”