I have a tensor with following symmetries
Clear[G]
G[i_, j_, k_, l_] := G[3 - i, 3 - j, 3 - k, 3 - l]
G[i_, j_, k_, l_] := G[j, i, l, k]
G[i_, j_, k_, l_] := Conjugate[G[k, l, i, j]]
where $i,\,j,\,k,\,l\in\{1,\,2\}$. It is fully specified by
G[1, 1, 1, 1] = r[1];
G[1, 1, 2, 2] = r[2];
G[1, 2, 1, 2] = r[3];
G[1, 2, 2, 1] = r[4];
G[1, 1, 1, 2] = z;
where $r\in\mathbb{R}$ and $z\in\mathbb{C}$. I would like to specify the whole tensor by writing
Array[G, {2, 2, 2, 2}]
This is obviously not possible due to infinite recursion. One can type all the elements manually. But is there an automatic way? Relation 2 can be specified with the help of SymmetrizedArray
, but I do not know how to specify 1 and 3.