Regular orthoscalar representations of the extended Dynkin graph E_8 and ∗-algebra associatedwith it - Kruhlyak, S. A.; Livins'kyi, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We obtain a classification of regular orthoscalar representations of the extended Dynkin graph E_8 with special character. Using this classification, we describe triples of self-adjoint operators A, B, and C such that their spectra are contained in the sets {0,1,2,3,4,5}, {0,2,4}, and {0,3}, respectively, and the equality A + B + C = 6I is true.