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Arnold's Trivium
1991 Arnold's Trivium
95
95
Part of
1991 Arnold's Trivium
Problems
(1)
Problem 95
Source:
7/1/2010
Decompose the space of homogeneous polynomials of degree
5
5
5
in
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
into irreducible subspaces invariant with respect to the rotation group
S
O
(
3
)
SO(3)
SO
(
3
)
.
algebra
polynomial
invariant
geometry
geometric transformation
rotation
quadratics