Abstract
The decomposition of the spinor bundle of the spin Grassmann manifolds Gm,n=SO(m+n)∕SO(m)×SO(n) into irreducible representations of so(m)⊕so(n) is presented. A universal construction is developed and the general statement is proven for G2k+1,3, G2k,4, and G2k+1,5 for all k. The decomposition is used to discuss properties of the spectrum and the eigenspaces of the Dirac operator.
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