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Spherical designs and finite group representations (some results of E. Bannai)

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Published in European Journal of Combinatorics. 2004, vol. 25, no. 2, p. 213 - 227
Abstract We reprove several results of Bannai concerning spherical t-designs and finite subgroups of orthogonal groups. These include criteria in terms of harmonic representations of subgroups of O(n) for the corresponding orbits to be t-designs (t = 0, 1, 2, 3,...) in Sn−1. We also discuss a conjecture of Bannai, dating from 1984, according to which t is bounded independently of the dimension n (for n ≥ 3) for such designs.
Keywords Spherical designsGroup representationsHomogeneous finite subgroups of orthogonal groups
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DE LA HARPE, Pierre, PACHE, Claude. Spherical designs and finite group representations (some results of E. Bannai). In: European Journal of Combinatorics, 2004, vol. 25, n° 2, p. 213 - 227. https://archive-ouverte.unige.ch/unige:12232

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Deposited on : 2010-10-22

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