I am trying to define a tensor $T$ which is antisymmetric under pair-wise exchange of its indices:
$T = \delta_{a],[b}\,\delta_{c],[d}\,\delta_{e],[f}\,\delta_{g],[h}$
where $T$ is antisymmetric under the exchanges $b \leftrightarrow c, d \leftrightarrow e, f \leftrightarrow g ,h \leftrightarrow a$.
I guess that defining $T$ as a Table will take too much memory. Maybe defining it as a function is better. In both cases I have no clue on how to do this in a clever, short way without writing down all possible exchanges by hand. Can you help?
$Assumptions = T \[Element] Arrays[{d, d, d, d, d, d}, Reals, Antisymmetric /@ Partition[RotateLeft@Range[6], 2]];
? $\endgroup$