The Discrete Dirac Identity on Hermitian Shells and Spectral Consequences for Hecke Operators

This archive contains the manuscript and verification scripts associated with: "The Discrete Dirac Identity on Hermitian Shells and Spectral Consequences for Hecke Operators" For every odd prime power q and every non-zero determinant shell O_mu in Herm_2(F_{q^2}), the paper proves the exact shell-cone identity d^† d = (A - (q - 1))(A + 1), where d is the shell-cone incidence operator from the massive shell to the punctured null cone, and A is the null-difference adjacency operator on the shell. The proof is entrywise and splits according to the geometric value of delta = det(X-Y), with separate treatment of the diagonal, null-adjacent, non-degenerate, antipodal, and degenerate non-antipodal cases. It uses…