Decomposition results for Gram matrix determinants
Abstract
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=Ππφ(π), with product over all associated partitions.
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