The Casimir eigenvalues on ad^{⊗ k} of SU(N) are linear on N

2025/06/16 by R. L. Mkrtchyan, Mkrtchyan, R. L.
Physics and Astronomy · #17B10 #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect

paper · pdf · doi:10.48550/arxiv.2506.13062

openalex publication_date 2025/06/16 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We consider eigenvalues of the Casimir operator on the naturally defined stable sequences of representations of su(N) algebra and prove that eigenvalues are linear over N iff λ₁+2λ₂+...+kλ_k=λ_N-1+2λ_N-2+...+kλ_N-k, where λ_i are Dynkin labels, and λ_i=0 for k<i></i>

Citations

• A universal dimension formula for complex simple Lie algebras

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