Index
Abstract polytope, 17
Adjacent
clusters, 37
orthants, 104
seeds, 39
Ambient field, 37
Associahedron, 17
acklund–Darboux transformation
(generalized), 201, 231
Borel
subalgebra, 5
subalgebra opposite, 5
Boundary measurement, 144, 179
map, 146, 179
Grassmannian, 160, 192
matrix, 146, 179
Bruhat
cell, 6
double, 6, 26
double Coxeter, 200
double reduced, 6, 26
opposite, 6
decomposition, 6
Cartan
companion, 50
matrix, 4, 49
Casimir element, 8, 107
Chevalley generators, 4
Cluster, 16, 37
adjacent, 37
algebra
coefficient-free, 41
compatible with a Poisson structure,
73
general, 43
of finite type, 49
of geometric type, 39
restriction of, 43
upper, 35, 47
with principal coefficients, 133
extended, 16, 37
manifold, 102
secondary, 113
monomial, 63
variable, 37
Cobracket, 10
1-cocycle condition, 9
Coefficient
group, 37
matrix
of a Poisson structure, 67
of a pre-symplectic structure, 111
Compatibility, 127
Concordance number, 143
Conjugate
horocycles, 115
segments, 122
Coxeter element, 200
Coxeter–Toda lattice, 200
Critical tree, 56
Cut, 175
base point of, 175
Cycle, 143
simple, 143
Cyclically dense, 16
Darboux transformation, 234
Diagram
cycle-like, 54
mutation, 53
of a mutation matrix, 52
tree-like, 54
Differential
left-invariant, 9
right-invariant, 9
Direct sum of networks, 187
Directed dual network, 167
Dynkin
diagram, 4
graph, 53
Edge weight, 142
modified, 176
Elementary reflection, 5
Exchange
graph, 40
243
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