2025/09/17 by R. L. Mkrtchyan, Mkrtchyan, R. L.
Physics and Astronomy · #17B20 #17B25 #17B40 #Experimental and Theoretical Physics Studies #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2509.13707
openalex publication_date 2025/09/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
We conjecture the connection between su and so members of universal, in Vogel's sense, multiplets. The key element is the notion of the \it vertical componentwise sum ⊕v of Young diagrams. Representations in the decomposition of the power of the adjoint representation of su(N) algebra can be parameterized by a couple of N-independent Young diagrams λ and τ, with equal area. We assume that the so(N) member of the universal (Casimir) multiplet of a given su(N) representation is the so representation with λ⊕v τ Young diagram. This allows one to obtain the universal form of the Casimir eigenvalue on that multiplet. Conjecture is checked for all known cases: universal decompositions of powers of adjoint up to fourth, and series of universal representations. On this basis we suggest the set of universal Casimirs for fifth power of adjoint. We also conjecture that vertical sum operation is a kind of the (dual version of the) folding map of Dynkin diagrams. This will hopefully explain the intrinsic symmetry of universal formulae with respect to the automorphisms of Dynkin diagrams.