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Set up the Gamma matrices of the Clifford algebra for SO(8) and SO(9) explicitly. Deduce the index structure, constraint
Posted: Fri Apr 29, 2022 11:00 am
by answerhappygod
- Set Up The Gamma Matrices Of The Clifford Algebra For So 8 And So 9 Explicitly Deduce The Index Structure Constraint 1 (48.58 KiB) Viewed 20 times
Set up the Gamma matrices of the Clifford algebra for SO(8) and SO(9) explicitly. Deduce the index structure, constraints and dimensions of the adjoint, Spinor-Vector and three index totally antisymmetric irreducible representations of SO(8) and SO(9). Deduce the quadratic indices (S2(R)) of these irreps of SO(8) and decompose them w.r.t the maximal subgroup SO(7) < SO(8). Show that the dimensions and quadratic indices match. Explain your procedure at each stage.