I am readin Belinte's book about Lie algebras (I have also the Cahn) .(adsbygoogle = window.adsbygoogle || []).push({});

And I try to understand this. He writes

"Each basic weight is invariant under all but one of the simple Weyl reflections since w_i l_j = l_j for i<>j while w_i l_i = l_i - alpha_i

(alpha_i issimpleby definition of simple reflections). Hence th Dynkin indices m' of the reflected weights w_j mu are related to the indices m_i of mu by m'_i = m_i - A_ij m_j"

Could you, please, tell me how to prove that w_i l_j = l_j for i<>j

thanks

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# A question about simple Weyl reflections

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