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Georgi writes that "

*A tensor operator is a set of operators that transforms under commutation with the generators of some Lie algebra like an irreducible representation of the algebra. [...] A tensor operator transforming under the spin-s representation of SU(2) consists of a set of operators, O^s_l, for l=1 to l = 2s+1(or -s to s), such that*:

[tex] [J_a, O^s_l] = O^s_m[J^s_a]_{ml}"[/tex]

I thought I understood 90-95% sofar in the book but I really dont see what he tries to define here.. Could somebody maybe help me and introduce the concept in Georgis way but with some more words and an example i will recognize from QM? I dont recognize what he is trying to construct from my QM courses.