I don't know what this symbol in root systems means (of coxeter groups) I'm reading Humphreys, Reflection groups and Coxeter groups. The section "Construction of root systems" and the books uses the symbol $ \mathop {\alpha}\limits^{\sim} $ to denote an special element. But I don't know what it is. I looked for it but there is nothing about it.


I believe it is just a formal symbol that represents the element. They wanted something that was a modified $\alpha$ for continuity reasons, and decided to go with that symbol for unknown reasons. It's the same as if they had written $\alpha'$ (or even $x$ for that matter)
