Homework - Week 12

• Prove g₂ so₇C and then analyze the embedding as follows:
  1. Exhibit S₃ (the symmetric group on 3 elements) as a group of automorphisms of so₈C.
  2. Show that the invariant algebra under this action is g₂.
  3. Hence embed g₂ as a subalgebra of so₇C. (Hint: S₂ is a subgroup of S₃.)
  4. Decompose the eight-dimensional spinor of so₇C into irreps of g₂.
  5. Do the same for the adjoint rep of so₇C.

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