My personal experience is that I came across the dual Coxeter number when I was studying the exceptional series of Lie algebras. I would need to look up the details and references but it was the dual Coxeter number that made the numerology work.

You have not mentioned that the dual Coxeter number is the Coxeter number of the dual root system (hence the terminology).

My personal experience is that I came across the dual Coxeter number when I was studying the exceptional series of Lie algebras. I would need to look up the details and references but it was the dual Coxeter number that made the numerology work.

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