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Is there any way to classify all the simple roots of $sl_n (\mathbb C)\ $?

I know that there $\frac {n^2 - n} {2}$ many positive roots and hence the same number of negative roots. But what is the basis of them?

ACB
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    This is done in probably every single textbook that deals with the subject. In any case, there is no such thing as the simple roots: you have to pick a positive ser of roots and that determines a corresponding set of simple roots. – Mariano Suárez-Álvarez Feb 14 '23 at 08:15
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    The duplicate has a very good answer by Torsten, including "basis roots". Of course, we may change the basis. The typical picture of type $A_2$, i.e., for $\mathfrak{sl}_3(\Bbb C)$, which is inlcuded there, is for the "standard" basis. – Dietrich Burde Feb 14 '23 at 09:03
  • @MarianoSuárez-Álvarez$:$ Which book are you referring to here? I haven't found any book which deals with the general case. Could you please tell one such? Thanks. – ACB Feb 14 '23 at 15:55
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    @AnilBagchi. Humphreys' "Introduction to Lie algebras", Erdmann & Wilson's book of the same name, Hall's book on Lie groups, Procesi, Fulton & Harris. All of these will construct explicit simple roots for $A_n$ – Callum Feb 14 '23 at 18:16

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