Say I have the product $A_iB_jC_kD_l$ which I know to be equal to $1$ iff $i=k$, $j=l$, and $i\ne j$. It equals $-1$ iff $i=l$, $j=k$, and $i\ne j$. And it equals $0$ otherwise. How do I write this in a compact notation? The $\pm 1$ or $0$ part reminds me of the Levi-Civita symbol, but I can't seem to think of a combination of Levi-Civita and Kronecker deltas that'll give me the right thing here.
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Possibly related: http://math.stackexchange.com/questions/1829624/constructing-an-expression-involving-kronecker-delta-and-levi-civita-symbol/1829641#1829641 – okrzysik Jul 08 '16 at 04:11
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Doesn't $(1-\delta_{ij})(\delta_{ik} \delta_{jl} - \delta_{il} \delta_{jk})$ work? I don't see how it could be simplified. Also, what are the possible values for the indices? – Derived Cats Jul 08 '16 at 04:23