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The Doublet Tower of Cl(4,2): Universal Nilpotency, Projector Identities, and the sl(8,R) Parabolic from Conformal Null Vectors
The conformal geometric algebra Cl(4,2) ~ R(8) carries a natural Z_2-grading defined by the dilatation bivector D=\e_4e_0, which satisfies $D^2=1$ and splits the eight-dimensional spinor module into two four-dimensional eigenspaces $S=S_+\oplus S_-$. We prove that the ad_D-eigenvectors of Cl(4,2), t
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