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)