The decomposition of the spinor bundle of Grassmann manifolds

Details The decomposition of the spinor bundle of Grassmann manifolds The decomposition of the spinor bundle of Grassmann manifolds

2007-10-17

arxiv.org/abs/0710.3245v2

J. Math. Phys. 48, 113511 (2007)

Mathematics

Differential Geometry

30 pages. v2 coincides with published version

Scientific paper

10.1063/1.2804760

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.

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