What are the length of the longest element in a Coexter group for every type?

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What are the length of the longest element in a Coxeter group for every type? Thank you very much.

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The length of the longest element is exactly the number of positive roots, so

  • Type $A_n$: ${n + 1} \choose 2$
  • Types $B_n, C_n$: $n^2$
  • Type $D_n$: $n^2 - n$
  • Type $I_2(n)$: n
  • Type $E_6$: 36
  • Type $E_7$: 63
  • Type $E_8$: 120
  • Type $F_4$: 24
  • Type $G_2$: 6
  • Type $H_3$: 15
  • Type $H_4$: 60