If I am not mistaken, it should be true that a type $A_n$ root system contains $n+1$ different sub-systems of type $A_{n-1}$. In my geometric application these do appear quite naturally, but is there an easy algebraic way to see this?
2026-03-26 17:32:19.1774546339
Number of type $A_{n-1}$ sub-systems of root system $A_n$
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