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marcus

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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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