is the special orthogonal group in dimension 12.
is the spin group in dimension 12.
In the classification of simple Lie groups this is the entry D6.
rotation groups in low dimensions:
see also
(…)
Discussion as a gauge group in grand unified theory (see there):
S. Rajpoot and P. Sithikong, Implications of the gauge symmetry for grand unification, Phys. Rev. D 23, 1649 (1981) (doi:10.1103/PhysRevD.23.1649)
Takaaki Nomura and Joe Sato, Standard(-like) Model from an Grand Unified Theory in six-dimensions with extra-space, Nucl.Phys.B811:109-122, 2009 (arXiv:0810.0898)
Takaaki Nomura, Physics beyond the standard model with extra-space, 2009 (pdf, pdf)
Cheng-Wei Chiang, Takaaki Nomura, Joe Sato, Gauge-Higgs unification models in six dimensions with extra space and GUT gauge symmetry (arXiv:1109.5835)
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