Decomposition results for Gram matrix determinants

@article{Banica2010DecompositionRF,
  title={Decomposition results for Gram matrix determinants},
  author={Teodor Banica and Stephen J. Curran},
  journal={Journal of Mathematical Physics},
  year={2010},
  volume={51},
  pages={113503}
}
We study the Gram matrix determinants for the groups Sn, On, Bn, Hn, for their free versions Sn+,On+,Bn+,Hn+, and for the half-liberated versions On*,Hn*. We first collect all the known computations of such determinants, along with complete and simplified proofs, and with generalizations where needed. We conjecture that all these determinants decompose as D = ∏πφ(π), with product over all associated partitions. 

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