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I've seen tensor methods in physics for finding lie group representations, as in Wu-Ki Tungs Group Theory in Physics, which uses tensors physics style, ie with indices; and Cvitonovics Birdtracks, Lie's and Exceptional Groups for finding irreducible representations of the classical lie groups, which uses a diagrammatic style.

Tung tackles only SO(2) & SO(3), whereas Cvitanovic tackles the classical Lie and exceptional groups.

Is there a exposition of the same in standard mathematicians language?

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What's not rigorous about indices and diagrams? Also, it would help if you actually stated a specific result you want to understand. Most of the people here aren't physicists and so don't know what "tensor methods in physics for finding Lie group representations" actually entails (are you merely writing down a list of representations or proving that these are all representations, etc.). –  Qiaochu Yuan Jun 14 '12 at 13:10
    
@Yuan:Ok, silly phrasing on my part. I'll edit it out. –  Mozibur Ullah Jun 14 '12 at 13:15
    
@all Are you asking for a "coordinate free" proof, instead of one that makes reference to components? –  rschwieb Jun 14 '12 at 21:41

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