Decomposition results for Gram matrix determinants
Abstract
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 halfliberated 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 = ∏_{π}φ(π), with product over all associated partitions.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 November 2010
 DOI:
 10.1063/1.3511332
 arXiv:
 arXiv:1009.4036
 Bibcode:
 2010JMP....51k3503B
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 18 pages