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Complementary group with respect to SO(n)

par Couvreur, G.;Deenen, Jacques ;Quesnea, C.
Référence Journal of mathematical physics, 24, 4, page (779-784)
Publication Publié, 1982

Article révisé par les pairs

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Résumé :

We look for a complementary group with respect to SO(n) within either irreducible representation (1/2dn) or (1/2dn-12/3) of the group Sp(2dn,R ) of linear canonical transformations in a 2dn-dimensional phase space. We prove that: (i) such a group is Sp(2d,R ) when n = 2q+1 or n = 2q>2d; (ii) it is SU(d,d) when n = 2 and d>1; (iii) it does not exist when n = 2, d = 1, or 2