I am a physicist, so my apologies if haven't framed the question in the proper mathematical sense.(adsbygoogle = window.adsbygoogle || []).push({});

Matrices are used as group representations. Matrices act on vectors. So in physics we use matrices to transform vectors and also to denote the symmetries of the vector space.

v_i = Sum M_ij v_j

Is there an equivalent group representation that act on tensors instead of vectors?

T_ij = Sum M_iajb T_ab

I guess then we need some group multiplication law...

may be

M_abcd = Sum M_axcy M_xbyd

Does this make any sense? Please provide some references where I can find more information.

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# Group representations on tensor basis.

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