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If [itex] \Lambda_i [/itex] is some element of the Lorentz group and [itex] \Lambda_j [/itex] is another, different element of the group then under multiplication....

[itex] \Lambda_i \Lambda_j [/itex] is also an element of the Lorentz group, say

[itex] \Lambda_i \Lambda_j =c_{ij}^k\Lambda_k[/itex]

where [itex] c_{ij}^k [/itex] has value 1 for one unique combination of i,j and k and 0 for the others and with a sum over k.

Now I appreciate the i,j and k should be continous but for the moment assume they are discrete because it's easier. i,j and k run over all the integers because there are infinitely many elements of the group.

How the hell do I find the [itex] c_{ij}^k [/itex]? I have absolutely no idea. My knowledge of rep theory is **** poor.