Go to previous page Go up  

Index

A+1+, 3, 3, 3, 4, 4, 5, 8
A++ 1, 4
BE10, 3, 4, 7
BE10, 7
DE10, 3, 4, 7
DE10, 4
E 10, 3, 4, 8, 8, 9, 9, 9, 10
E10, 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

Vogan diagram, 6, 6, 6, 6
Vogan diagram, 6

Weyl chamber, 5, 5, 5, 10
Weyl chamber, 4


  Go to previous page Go up