Recollement of D-module categories via Kirwan-Ness stratifications on cotangent stacks — E8 Intelligence Research

FINDING: Recollement for D-module categories on algebraic stacks via Kirwan-Ness stratifications of cotangent stacks, yielding a gluing decomposition from unstable strata. | MATH: Recollement = exact sequence of triangulated categories \( D^b(Y) → D^b(Y^∘) → D^b(Y Y^∘) \) with adjoint functors; Kirwan-Ness stratification indexed by dominant weights \(λ ∈ Λ^+\) in the Weyl chamber; strata \(S_λ ⊂ T^*Y\) defined by moment map \(μ⁻¹(0)\) and gradient flow; twisted D-modules \(D_χ\) with twist \(χ ∈ H^2(Y,C^*)\); subquotient categories = microsupported modules on conormal bundles \(T^*S_λY\). | CONNECTION: Dominant weights \(λ\) live in the Weyl chamber — a fundamental domain of the affine Weyl group, whose walls are hyperplanes at angles \(π/2, π/3, π/4, π/6\) (crystallographic root systems A_n, B_n, C_n, D_n, E_6, E_7, E_8, F_4, G_2). The stratification is a Morse-theoretic analogue: cri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com