'Paraparticles' Would Be a Third Kingdom of Quantum Particle

Here's a link to the paper: https://www.nature.com/articles/s41586-024-08262-7

I really wish they tied this into representation theory, because it looks like the R-tensors are similar to representations of the permutation group, but I don't see exactly how to write them in terms of representations.

The r-tensors are a representation of the symmetric group, and this is stated right after eqn. 4.