Representations of Algebras Defined by a Multiplicative Relation and Corresponding to the Extended Dynkin Graphs D_4, E_6, E_7, E_8 - Livins'kyi, I. V.; Radchenko, D. V. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We describe, up to unitary equivalence, all k-tuples (A_1, A_2,..., A_k) of unitary operators such that A^n_i_i = I for i = 1, k and A_1 A_2 ... A_k = λ I, where the parameters (n_1,... ,n_k) correspond to one of the extended Dynkin diagrams D_4, E_6, E_7, E_8, and λ C is a fixed root of unity.