Index of terminology

The reference numbers indicate the chapter, paragraph and number (or, exceptionally, exercise), respectively.

Adjoining chambers: IV, 1. Exercise 15. Affine (Weyl group): VI, 2, 1. Alcove: VI, 2, 1. Angle between two roots: VI, 1, 2. Anti-invariant: V, 5, 4 and VI, 3, 3. Apartment: IV, 1, Exercise 15. Arrow: IV. Appendix, 1. Associated (bilinear form to a Coxeter system): V, 4, 1. Basis of a root system: VI, 1, 5. Building: IV, 1, Exercise 15. Canonical bilinear form: VI, 1, 12. Canonical Cartan matrix: VI, 1, 5. Cartan matrix: VI, 1, 5. Chain: IV, Appendix, 3. Chain of roots: VI, 1, 3. Chamber: V, 1, 3 and V, 3, 1. Chamber of a building: IV, 1, Exercise 15. Characteristic degrees: V, 5, 1. Circuit: IV, Appendix, 3. Closed set of roots: VI, 1, 7. Compact hyperbolic (Coxeter group of ... type): V, 4, Exercise 12. Components (connected of a graph): IV, Appendix, 2. Components (irreducible of a Coxeter system): IV, 1, 9. Conjugate elements of a group: IV, 1, 3. Connected graph: IV, Appendix, 2. Connection index: VI, 1, 9. Contragredient representation: V, 4, 4. Cosets (double): IV, 2, 1. Coxeter graph: IV, 1, 9. Coxeter group: IV, 1, 3. Coxeter matrix: IV, 1, 9.

Coxeter number: V, 6, 1 and VI, 1, 11. Coxeter system: IV, 1, 3. Coxeter transformation: V, 6, 1 and VI, 1, 11. Crystallographic group: VI, 2, 5. Dihedral group: IV, 1, 2. Dominant weight: VI, 1, 10. Dynkin graph: VI, 4, 2. Essential group generated by reflections: V, 3, 7. Exchange condition: IV, 1, 5. Exponents of a finite Coxeter group: V, 6, 2. Face of a chamber: V, 1, 4. Facet: V, 1, 2. Fundamental weight: VI, 1, 10. Forest: IV, Appendix, 3. Gallery: IV, 1, Exercise 15. Graph: IV, Appendix, 1. Graph (completed Dynkin): VI, 4, 3. Graph (Coxeter): IV, 1, 9. Graph (Dynkin): VI, 4, 2. Half-space: V, 1, 1. Hecke algebra: V, 2, Exercise 22. Highest root: VI, 1, 8. Hyperbolic (Coxeter group of type): V, 1, Exercise 12. Hyperplane of a pseudo-reflection: V, 2, 1. Indivisible root: VI, 1, 3. Inverse system of roots: VI, 1, 1. Irreducible group generated by reflections: V, 3, 7. Irreducible Coxeter system: IV, 1, 9. Irreducible root system: VI, 1, 2. Joined vertices of a graph: IV, Appendix, 1. Length of a path in a graph: IV, Appendix, 2. Length of an element of a group: IV, 1, 1. Length of a root: VI, 1, 2. Minuscule weight: VI, 1, Exercise 24. Normaliser: IV, 2, 6. Normed graph: VI, 4, 2. Opposed facets: IV, 1, Exercise 18. Path: IV, Appendix, 2. Poincaré series: V, 5, 1. Polynomial (graded algebra): V, 5, 1. Positive root: VI, 1, 6. Presentation of a group: IV, 1, 3. Pseudo-reflection: V, 2, 1. Radical weights: VI, 1, 9.

Ramification point of a graph: IV, Appendix, 1. Rank of a root system: VI, 1, 1. Reduced decomposition: IV, 1, 1. Reduced root system: VI, 1, 4. Reflection: V, 2, 2. Representation associated to a Cartan matrix: V, 4, 3. Restricted direct product: IV, 1, 9. Root system: VI, 1, 1. Saturated set of weights: VI, 1, Exercise 23. Sign of an element of a Coxeter group: IV, 1, 3. Simply-transitive group action: IV, 2, Exercise 3. Simplex: V, 1, 6. Simplicial cone: V, 1, 6. Spacious building: IV, 1, Exercise 24. Special point: V, 3, 10. Strongly orthogonal roots: VI, 1, 3. Structured building: IV, 1, Exercise 24. Subgraph: IV, Appendix, 1. Support of a facet: V, 1, 2. Terminal vertex of a graph: IV, Appendix, 1. Tits subgroup: IV, 2, Exercise 3. Tits' theorem: V, 4, 4. Tree: IV, Appendix, 3. Vector of a pseudo-reflection: V, 2, 1. Vertex of a graph: IV, Appendix, 1. Wall of a chamber: V, 1, 4. Weights: VI, 1, 9. Weyl group of a root system: VI, 1, 1. Weyl group of a Tits system: IV, 2, 1.