Schur polynomials twisted by roots of unity and reciprocal pairs: torsion filters, fusion quotients, and total unimodularity at odd order

What the math gives to ML

The paper provides an exact algebraic construction for evaluating Schur characters on a cyclic root-of-unity orbit augmented by reciprocal pairs. Its transferable asset is not the particular representation-theoretic classification, but the combination of cyclic torsion filtering, inversion symmetry, and determinant-based cancellation: features can be projected onto selected residue classes or symmetry sectors with exact zeroing rather than learned cancellation. A practical neural adaptation is a structured feature layer for cyclic or periodic data that computes symmetric-polynomial statistics of learned reciprocal latent pairs and applies a roots-of-unity Fourier projector. This is most plausible when exact cyclic invariance or separation of congruence sectors matters, such as graph signals on cycles, periodic time series, or equivariant token mixing.