How define a general tensor symmetry

Question

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}

Thank you for the advice.

Comments

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

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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.

Answer 1

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!

Cheers.