• Corpus ID: 119186858

Geometry and Physics of Sp(3)/Sp(1)^3

  title={Geometry and Physics of Sp(3)/Sp(1)^3},
  author={B. E. Eichinger},
  journal={arXiv: General Physics},
  • B. Eichinger
  • Published 27 April 2018
  • Mathematics
  • arXiv: General Physics
The action of $Sp(3)$ on a vector space $V_3\in \mathbb H^3$ is analyzed. The transitive action of the group is conveyed by the flag manifold (coset space) $Sp(3)/Sp(1)^3\sim G/H$, a Wallach space. The curvature two-forms are shown to mediate pair-wise interactions between the components of the $\mathbb H^3$ vector space. The root space of the flag manifold is shown to be isomorphic to that of $SU(3)$, suggesting similarities between the representations of the flag manifold and those of $SU(3… 

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