, 3, 3, 3, 4, 4, 5, 8

, 4

, 3, 4, 7

, 7

, 3, 4, 7

, 4

, 3, 4, 8, 8, 9, 9, 9, 10

, 4, 4

, 4

, 3, 4, 7

, 7

, 3, 4, 7

, 4

, 3, 4, 8, 8, 9, 9, 9, 10

, 4, 4

billiard wall, 2, 2, 2, 2, 2, 3, 5, 5, 5

billiard wall, 2

BKL-limit, 2, 2, 5, 5, 5, 5, 9, 9, 9, 10

BKL-limit, 2

Borel subalgebra, 7, 9

Borel subalgebra, 5

Cartan conjugation, 6

Cartan involution, 6, 6, 6, 6, 6, 6, 7, 9, 2

Cartan involution, 6

Cartan matrix, 4, 4, 4, 5, 5, 7, 7, 8, 8, 10, 10

Cartan matrix, 4

Cartan subalgebra, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 9, 10

Cartan subalgebra, 4

Chevalley involution, 9, 9

Chevalley involution, 4

coset space, 5, 5, 5, 7, 9, 9, 9, 9

coset space, 9

cosmological billiard, 2, 2, 2, 2, 2, 3, 5, 5, 5, 7, 7, 7, 10

cosmological billiard, 2, 2

Coxeter graph, 3, 3, 4

Coxeter graph, 3

Coxeter group, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 10

Coxeter group, 3

Dynkin diagram, 4, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 10, 10

Dynkin diagram, 4

Dynkin labels, 8, 8, 8, 8, 8

Dynkin labels, 8

generalized metric, 9

generalized metric, 9

geometric configuration, 10, 10, 10

geometric configuration, 10

geometric reflection, 3, 3, 3, 5, 5

geometric reflection, 2, 5

Hamiltonian constraint, 2, 2, 2, 9, 9, 9

hyperbolic space, 1, 3, 3, 5, 5

hyperbolic space, 2

intersection rules, 10, 10

intersection rules, 10

Iwasawa decomposition, 2, 5, 5, 6, 6, 6, 6, 7, 7, 7, 9, 9

Iwasawa decomposition, 2, 5

Kac–Moody algebra, 4, 5, 5, 8, 8, 8, 9, 9, 10

Kac–Moody algebra, 4

level decomposition, 8, 8, 8, 8, 8, 9, 9

level decomposition, 8

line incidence diagram, 10, 10

line incidence diagram, 10

Maurer–Cartan form, 9

maximal compact subalgebra, 7

maximal compact subalgebra, 9

maximal compact subgroup, 5, 5, 9

maximal compact subgroup, 9

nonlinear realisation, 9, 9

nonlinear realisation, 9

nonlinear sigma model, 5, 6, 7, 9, 9, 9

nonlinear sigma model, 9

outer multiplicity, 8, 8

outer multiplicity, 8

overextension, 4, 4, 4, 4, 4, 4, 5, 7, 7, 8

overextension, 4

regular subalgebra, 4, 4, 4, 8, 8, 9, 10, 10, 10

regular subalgebra, 4

restricted root system, 6, 7, 7, 7, 7, 7, 7, 7

restricted root system, 6

root, 3, 3, 4, 4, 4, 5, 5

root lattice, 4

root lattice, 4

root, 3, 4

scale-factor space, 3, 5, 9, 9, 9

scale-factor space, 2

Serre relations, 4, 8, 8

Serre relations, 4

Tits–Satake diagram, 6, 6, 6, 6, 6, 6, 6, 6

Tits–Satake diagram, 6

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