A Closed-Form Identity for the Post-Vanishing Cayley Carrier on Odd Dihedral Groups

Let Γ be a finite group and S = S−1 a non-central conjugacy class generating Γ. The full-context relation module on the Cayley digraph Cay(Γ, S) generates, by orthogonal complement and wedge-component projection inside the σ-anti-invariant ambient, a finite-dimensional Γ-module under based conjugation: the post-vanishing Cayley carrier E(2),πx,full(Cay(Γ, S))−. This paper studies its representation-theoretic structure. The main result is a closed-form regular-representation identity on the entir