Glider Representations: Hierarchical Clifford Theory for Normal Subgroup Chains — E8 Intelligence Research

FINDING: Clifford theory extended to chains of normal subgroups yields "glider representations" — a hierarchical decomposition of group representations that generalizes classical Clifford theory for semidirect products like Z²⋊D₄. | MATH: Classical Clifford: for H⊲G, Res_H^G(S) decomposes into H-simple modules; glider version: for chain 1⊲G₁⊲⋯⊲G_d=G, representations fragment into "gliders" along the chain. Key structure: semidirect product Z²⋊D₄ (lattice translations ⋊ square dihedral group) — the stabilizer group for a square lattice, relevant to quantum error-correcting codes (surface codes, toric codes). No explicit numerical constants given; the mathematics is structural (group cohomology, induction/restriction functors, Mackey decomposition). | CONNECTION: Z²⋊D₄ is the full crystallographic symmetry group (p4m) of the square lattice — its irreducible representations classify Bloch states in 2D periodic systems. The chain of normal subgroups mirrors hierarchical symmetry breaking: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com