Vol. 7, No. 3, 2019

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Effective computation of $\operatorname{SO}(3)$ and $\mathrm{O}(3)$ linear representation symmetry classes

Marc Olive

Vol. 7 (2019), No. 3, 203–237
Abstract

We propose a general algorithm to compute all the symmetry classes of any SO(3) or O(3) linear representation. This method relies on a binary operator between sets of conjugacy classes of closed subgroups, called the clips. We compute explicit tables for this operation, which allows us to definitively solve the problem.

Keywords
isotropy classes, clips, linear representations, symmetry classes, tensorial representations
Mathematical Subject Classification 2010
Primary: 20C35, 22C05
Milestones
Received: 4 January 2019
Revised: 16 June 2019
Accepted: 2 September 2019
Published: 14 September 2019

Communicated by Francesco dell'Isola
Authors
Marc Olive
Laboratoire de Mécanique et Technologie
École Normale Supérieure Paris-Saclay
Centre National de la Recherche Scientifique
Université Paris-Saclay
Cachan
France