Index of notation

The reference numbers indicate the chapter, paragraph and number, respectively.

$A_l$ (root system of type): VI. 4. 1; VI. 4. 7 and Plate I. $\tilde{A}_l$ : VI. 4. 3. $A[P]$ : VI. 3. 1. $\Lambda(R)$: VI. 1. 1. $\tilde{\alpha}$ (highest root): VI. 1. 8; VI. 4. 3. $\alpha_0 = -\tilde{\alpha}$ : VI. 4. 3. $(\alpha_1, \ldots, \alpha_l)$: VI. 1. 5. $B$ : IV. 2. 1. $B(C)$ (basis defined by the chamber C): VI. 1. 5. $B_l$ (root system of type): VI. 4. 1; VI. 4. 5 and Plate II. $\tilde{B}_l$ : VI. 4. 3. $B_M$ (bilinear form associated to the Coxeter matrix M): V. 4. 1. $C$ (chamber): V. 1. 3; VI. 1. 5. $c$ (Coxeter transformation): V. 6. 1; VI. 1. 11. $C_l$ (root system of type): VI. 4. 1; VI. 4. 6 and Plate III. $\tilde{C}_l$ : VI. 4. 3. $\gamma_i, \Gamma_C$ : VI. 2. 3. $\gamma(R)$: VI. 1. 12. $d = \prod_{\alpha > 0} (e^{\alpha/2} - e^{-\alpha/2})$: VI. 3. 3. $D_l$ (root system of type): VI. 4. 1; VI. 4. 8 and Plate IV. $\tilde{D}_l$: VI. 4. 3. $E$: VI. 4. 4. $E_6, E_7, E_8$ (root system of type): VI. 4. 7; VI. 4. 10; VI. 4. 11; VI. 4. 12 and Plates V, VI, VII. $\tilde{E}_6, \tilde{E}_7, \tilde{E}_8$: VI. 4. 3. $\varepsilon_1, \ldots, \varepsilon_n$: VI. 4. 4. $F_4$ (root system of type): VI. 4. 1; VI. 4. 9 and Plate VIII. $\tilde{F}_4$: VI. 4. 3. $G$: VI. 2. 3. $G_2$ (root system of type): VI. 4. 1; VI. 4. 13 and Plate IX. $\tilde{G}_2$ : VI. 4. 3. $\mathfrak{H}$ : V. 3. 1.

$h$ (Coxeter number): V, 6, 1; VI, 1, 11. $H_3, H_4$ (Coxeter systems of type): VI, 4, 1. $I_2(p)$ (Coxeter system of type): VI, 4, 1. $J(c^p) = \sum_{w \in W} \det(w) e^{w(p)}$ : VI, 3, 3. $L_0, L_1, L_2, L_3$ (lattices in $\mathbf{R}^n$): VI, 4, 4. $l(w), l_S(w)$ (length of an element w): IV, 1, 1. $m(s, s')$ : IV, 1, 9. $N$ : IV, 2, 1. $P(R)$ : VI, 1, 9. $Q(R)$ : VI, 1, 9. $R$ (root system): VI, 1, 1. $R'$ : VI, 1, 1. $\rho= \frac{1}{2} \sum_{\alpha> 0} \alpha$ : VI, 1, 10; VI, 3, 3. $S$ : IV, 1, 1. $S(c^p) = \sum_{q \in W.p} e^q$: VI, 3, 4. $S_w$ : IV, 1, 8. $T = B \cap N$ : IV, 2, 1. $V$ : VI, 1, 1; VI, 4, 4. $W = N/T$ : IV, 2, 1. $W$ : V, 3, 1. $w_0$ : VI, 1, 6. $W(R)$: VI, 1, 1. $W^+(R)$: VI, 4, Exercises. $W_X$ : IV, 1, 8. $\Phi_R$ : VI, 1, 12. $(\omega_1, \ldots, \omega_l)$: VI, 1, 10.