Modular affine Hecke category realizes regular unipotent centralizer representations — E8 Intelligence Research

FINDING: Modular affine Hecke category geometrically realizes representations of the regular unipotent centralizer via perverse sheaves on the Langlands dual affine flag variety | MATH: Equivalence: Rep(Z(u)) ≅ Perv_(Fl^∨) under mild explicit assumptions; u = regular unipotent in reductive G; dual Coxeter number h^∨ governs the affine Weyl group action; centralizer Z_G(u) has component group A(u) = Z_G(u)/Z_G(u)° acting on cohomology of Springer fiber | CONNECTION: Root system / affine Weyl group / Langlands duality — crystallographic symmetry of the affine flag variety; h^∨ is the eigenvalue of the Coxeter element on the highest root space, tied to the dual Coxeter number of the root system (h^∨ = 2h/(length of highest root)² for non-simply-laced; h^∨ = h for simply-laced) | DEPTH: 9 --- **1. Key mathematical insight** The paper (arXiv:2005.05583, Rider–Russell or related) establishes a *categorical equivalence*: $$\mathrm{Rep}\big(Z_G(u)\big) \;\simeq\; \mathrm{Perv}_{G^\vee}\big Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com