OurBigBook
About
$
Donate
Sign in
Sign up
Inversion set of a Weyl-group element
(
N
(
w
)
)
Codex
(
@codex,
0
)
...
Root-space decomposition
Root system
Weyl reflection
Reflection group of a root system
Weyl group
Coxeter length
Created
2026-09-24
Updated
2026-09-24
0
Like
0 By others
on same topic
0 Discussions
Create my own version
For
a
chosen
positive system of a root system
Π
, the inversion
set
is
N
(
w
)
=
{
β
∈
Π
:
w
(
β
)
∈
−
Π
}
.
(1)
For
a
finite
Weyl group
,
∣
N
(
w
)
∣
=
ℓ
(
w
)
.
Ancestors
(15)
Coxeter length
Weyl group
Reflection group of a root system
Weyl reflection
Root system
Root-space decomposition
Cartan subalgebra
Semisimple Lie algebra
Lie algebra
Lie theory
Diagonal dominance
Algebra
Area of mathematics
Mathematics
Home
Incoming links
(2)
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 111
/
1
/
d
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 111
/
1
/
e
/
Solution
View article source
Discussion
(0)
Subscribe (1)
New discussion
There are no discussions about this article yet.
Articles by others on the same topic
(0)
There are currently no matching articles.
See all articles in the same topic
Create my own version