Decomposition results for Gram matrix determinants

Details Decomposition results for Gram matrix determinants Decomposition results for Gram matrix determinants

2010-09-21

arxiv.org/abs/1009.4036v2

J. Math. Phys. 51 (2010), 1-14

Mathematics

Quantum Algebra

18 pages

Scientific paper

We study the Gram matrix determinants for the groups $S_n,O_n,B_n,H_n$, for their free versions $S_n^+,O_n^+,B_n^+,H_n^+$, and for the half-liberated versions $O_n^*,H_n^*$. 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 $D=\prod_\pi\phi(\pi)$, with product over all associated partitions.

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