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Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 4
/
19I
/
a
/
iii
/
Solution
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2018
ii
Paper 4
19I
a
iii
Created
2026-09-24
Updated
2026-10-03
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The
weights
of
V
2
are
z
2
,
1
,
z
−
2
. Degree-three
monomials
in these
weights
show that the character of the
symmetric power
S
3
V
2
has
weights
z
6
+
z
4
+
2
z
2
+
2
+
2
z
−
2
+
z
−
4
+
z
−
6
=
χ
V
6
+
χ
V
2
.
(1)
Characters determine
finite-dimensional
S
U
(
2
)
representations, hence
S
3
V
2
≅
V
6
⊕
V
2
.
(2)
Ancestors
(12)
iii
a
19I
Paper 4
ii
2018
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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