Index of notations
We mostly follow the conventions and notations of Bourbaki; in particular:
X cY
X^Y
Z
N = Z
+
N
+
= Z
+ +
Q
R
R
+
R
+ +
Card(X), \X\
X is a subset of Y
X is a proper subset of Y
rational integers
natural numbers including 0
positive natural numbers
rational numbers
real numbers
nonnegative real numbers
positive real numbers
cardinality of set X
Specific notations ocurring in the text are listed in the following table.
Symbol Explanation Section Page
, )
( ^
( ) v
( ) c
( ) °
©i€/
2 '
2(/)
2./)
JK
4A
[*-[
~ s , ~
Nil,
a v
aT (3
a h / 3
e(R),
Ri
*s
ll/lloc
or /? H a
e*(R)
canonical pairing
set of vectors orthogonal to ( )
coroot system functor
additive closure of ( )
polar of a set ( )
direct sum of root systems
group of sign changes
finitary sign changes
finitary even sign changes
symmetric difference
preorder induced by A
principal final segment
equivalence relations defined by S
1-norm, oo-norm
coroot
a is collinear to /?
a governs (3
quotients of weight groups
3.1
3.5
4.9
10.2
B.l
3.10
8.9
9.4
9.4
9.1
10.7
B.2
12.3
15.4
3.3
11.16
11.16
7.3
21
22
33
86
189
25
72
76
79
75
88
190
111
148
21
107
107
54
205
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