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This paper deals with certain aspects of a conjecture made by B. Kostant in 1983 relating the Coxeter number to the occurrence of the simple finite groups L(2, q) in simple complex Lie groups. A unified approach to Kostant's conjecture that yields very general results for the rank two case is presented.

𝐿₂(𝑞) and the rank two Lie groups: their construction in light of Kostant’s conjecture