Theorem on the Embedding of the SU(n) Hierarchy into the Deligne Exceptional Series

We prove that all values of the exact polynomial n(k) = (103k⁴ − 370k³ + 101k² + 478k)/12 for k ∈ {−1, 0, 1, 2, 3} belong to the classical Deligne exceptional series D = {0, 1, 2, 3, 4, 6, 8, 9, 10, 14, 20, 26, 32, 52, 58, 78, 133, 190, 248}. Key results:- Theorem 1: All n(k) for k = -1, 0, 1, 2, 3 belong to the classical Deligne series.- Proposition 1: Probability of random coincidence p < 5×10⁻⁴ excludes the randomness hypothesis.- Proposition 2: Adjoint dimensions for k = -1, 1, 3 belong to the extended Deligne series.- Proposition 3: n(3) = 58 = 26 + 32 reflects the structure SU(58) = SU(26)×SU(32)×U(1). Languages: Russian, EnglishLicense: UAL v1.0 (CC BY-NC-ND 4.0 equivalent)