Irreducible Representations of so(4,C)

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Does anyone know how to classify the finite-dimensional irreducible representations of so(4,C)? Can they all be built from irreducible reps of sl(2,C) given the fact that so(4,C) \cong sl(2,C) \times sl(2,C).

Thanks!
 
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It depends on what you mean by "built from"!

For an explicit discussion of the representations of so(4,C) (and IIRC so(n,C) for n<8) see Fulton and Harris's Representation Theory.
 
Thanks morphism.

By "build from" I meant taking a tensor product of sl(2,C) modules.

I'll give Fulton and Harris another look.

Thanks again.
 

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