Symmetry-Resolved Sensitivity Redistribution Under Tensor Lifting in Electromagnetic Sensing Architectures

Symmetric electromagnetic sensing architectures induce representation-space decompositions that organize how measured fields respond to rotations, reflections, and programmable configurations. This paper develops a symmetry-resolved framework for analyzing how local parameter sensitivity is distributed across irreducible sectors and how this distribution changes under tensor lifting. Character-weighted Reynolds projectors decompose the derivatives of first-, second-, and fourth-order observables into orthogonal isotypic components, whose relative weights are quantified through normalized entropy, effective-sector occupancy, and dominant-sector concentration. The formulation distinguishes algebraic sector accessibility, determined by induced representations and tensor-product fusion, from the sensitivity profile realized by a specific physical observation model. The framework is validated using a narrowband far-field electromagnetic model of a two-ring C4-symmetric receiving array and is further examined through matched cyclic and dihedral array ensembles. The results reveal a robust redistribution of sensitivity under tensor lifting in the tested cyclic architectures, while the dihedral configurations exhibit a different, order-dependent behavior associated with their richer representation structure. These findings do not imply a universal increase in information or estimation performance; rather, they show that tensorization reorganizes the symmetry channels through which local sensitivity is expressed. The proposed framework provides a diagnostic tool for comparing and designing symmetry-aware antenna arrays, metasurfaces, reconfigurable intelligent surfaces, and related programmable sensing architectures.