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Let φ SU(2) ---> SO(3) be the double covering
Any irreducible representation of SO(3) pulls back by φ
to provide an irreducible representation of SU(2) on the
same finite dimensional Hilbert space.
this seems clear, almost not worth saying:
the pullback is obviously irred. and has the same dimension.
I have a question about the other direction----suppose an
irred. rep. of SU(2) factors thru φ
then it obviously gives a representation of SO(3), same space
same dimension and all, but
under what circumstances is the representation irreducible?
Any irreducible representation of SO(3) pulls back by φ
to provide an irreducible representation of SU(2) on the
same finite dimensional Hilbert space.
this seems clear, almost not worth saying:
the pullback is obviously irred. and has the same dimension.
I have a question about the other direction----suppose an
irred. rep. of SU(2) factors thru φ
then it obviously gives a representation of SO(3), same space
same dimension and all, but
under what circumstances is the representation irreducible?
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