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

Abstract

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 \( D^b(Y) \to D^b(Y^\circ) \to D^b(Y\setminus Y^\circ) \) with adjoint functors; Kirwan-Ness stratification indexed by dominant weights \(\lambda \in \Lambda^+\) in the Weyl chamber; strata \(S_\lambda \subset T^*Y\) defined by moment map \(\mu^{-1}(0)\) and gradient flow; twisted D-modules \(\mathcal{D}_\chi\) with twist \(\chi \in H^2(Y,\mathbb{C}^*)\); subquotient categories = microsupported modules on conormal bundles \(T^*_{S_\lambda}Y\). | CONNECTION: Dominant weights \(\lambda\) live in the Weyl chamber — a fundamental domain of the affine Weyl group, whose walls are hyperplanes at angles \(\pi/2, \pi/3, \pi/4, \pi/6\) (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