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Scientific article
English

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

Published inEuropean journal of combinatorics, vol. 25, no. 2, p. 213-227
Publication date2004
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 designs
  • Group representations
  • Homogeneous finite subgroups of orthogonal groups
Citation (ISO format)
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. doi: 10.1016/S0195-6698(03)00101-X
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ISSN of the journal0195-6698
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