The decomposition of the spinor bundle of Grassmann manifolds

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Klinker, Frank
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Abstract
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The decomposition of the spinor bundle of the spin Grassmann manifolds $G_{m,n}=SO(m+n)/SO(m)\times SO(n)$ into irreducible representations of $\mathfrak{so}(m)\oplus\mathfrak{so}(n)$ is presented. A universal construction is developed and the general statement is proven for $G_{2k+1,3}$, $G_{2k,4}$, and $G_{2k+1,5}$ for all $k$. The decomposition is used to discuss properties of the spectrum and the eigenspaces of the Dirac operator.
Comment: 30 pages. v2 coincides with published version
Keywords
Mathematics - Differential Geometry, Mathematical Physics, 17B10, 14M14, 53C27
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