Index
A-basis 17
additively closed 85
alternating group 78
automorphism
—, outer 79
of root system 24
automorphism group 24, 79, 80
—, of coroot system 35
—, outer 39
Basic (co)weight 59
of simple root systems 73
basis
(see also root basis)
—, adapted 17
—, integral 47
big Weyl group 39, 79, 82
bound 14
bounded 14
—, locally finite root system 22
—, strongly 15, 16, 48
coweight 54
linear form 148
weight 54
Cardinal 40, 143
successor 40
Cart an
matrix 50
number 22, 185
category
of quotients of root systems by full sub-
systems 48
of root systems and embeddings 23
of root systems and morphisms 23
of sets in vector spaces 6
of symmetric sets in real vector spaces
85
chain
—, connecting 26
closed
—, additively 85
subsystem 86
closure
—, additive 86
of facet 151
coequalizer 12
colimit
—, filtered, in R S E 27
in SVfc 13
collinear 107, 174, 176
collinear system 66
completely reducible (Weyl group) 41
cone
—, dual, of parabolic subset 146
—, of type D 194
—, proper 89, 189
of type A 193
of type B 190
spanned by parabolic subset 94, 97
spanned by unipotent subset 94
connected 26
component 26
parabolic subset 101
subset 26
coproduct
in R S 25
in SVfc 6
corank 9
core 7
coroot 21
coroot system 33
coset 9
cotrace 65
coweight 53, 70, 71
(see also weight)
—, basic 59, 73, 148
—, bounded 54, 148
—, distinguished 172
—, dominant 153
—, dual 59
—, fundamental 153
—, indivisible 59
—, minuscule 61, 73, 168
—, quasi-minuscule 172
—, radicial 53
fundamental 157
Coxeter
graph 46
group 46, 84
system 45, 46, 50
cycle
—, positive, negative 76
—, signed type 76
D a t u m
—, /-datum 120
—, p-datum 134
defined over Q 93
diamond 175
211
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