# How define a general tensor symmetry

+1 vote

Hi, can you define a general tensor symmetry?

Some simpler symmetry can be defined using the TableauSymmetry, but I have not figured out how to define a more complex one. I admit that young tableaux was too unreasonable. How to define a general symmetry tensor?
Specifically, I need to define a tensor with this symmetry:

A_{a b c i j k} = A_{i j k a b c}
A_{a b c i j k} = - A_{a c b i j k}
A_{a b c i k j} = - A_{a b c i k j}


That last line is probably A_{a b c i j k} = - A_{a b c i k j} ?

yes, last line is

A_{a b c i j k} = - A_{a b c i k j}


sorry for typo mistake. But this symmetry is redundant if the two previous ones are valid.

With the provided information, you cannot determine an irrep under which your tensor transform. That's why you cannot use TableauSymmetry
Notice however that, your tensor could lie on the {2,2,2} Young tableau. Perhaps that can help!