If we take a tensor product of copies of of the same vector space V and its dual, then we have a natural action of GL(V) and any subgroup G (for example the orthogonal group or something more complicated).
Wheeled PROPs were introduced by Markl, Merkulov and Shadrin, and seem to be the right framework to study G-invariant tensors, their representations as tensor networks and the algebraic relations among
such invariant tensors. This is joint work with Visu Makam.
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