It's an invariant tensor of SL(3). The invariant symbol of SL(N) is epsilon with N indices. SU(N) inherits as a subgroup.
taking derivatives componentwise and also it’s an invariant tensor of SU(N)
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I'm pretty sure the epsilon tensor is only an invariant of SU(N) not SL(N) .. The δ_{i \bar{j}} is an SL(N) invariant
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Used like crazy in continuum mechanics
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