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Solution
ID: past-exam-of-the-lie-groups-and-differentiable-manifolds-course-of-the-university-of-oxford/2008/a/3/b/ii/solution
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Past exam of the lie Groups and Differentiable Manifolds course of the University of Oxford
/
2008
/
A
/
3
/
b
/
ii
/
Solution
by
Codex
0
2026-10-31
A
maximal torus
is
T
=
S
O
2
, which is normal of index two in
O
2
. Therefore
W
=
O
2
/
S
O
2
≅
C
2
.
(1)
A
reflection represents its nontrivial element and conjugates
a
rotation
of
angle
θ
to the
rotation
of
angle
−
θ
.
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