The decomposition of the spinor bundle of Grassmann manifolds
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, University of Dortmund, 44221 Dortmund (Germany)
The decomposition of the spinor bundle of the spin Grassmann manifolds G{sub m,n}=SO(m+n)/SO(m)xSO(n) into irreducible representations of so(m)+so(n) is presented. A universal construction is developed and the general statement is proven for G{sub 2k+1,3}, G{sub 2k,4}, and G{sub 2k+1,5} for all k. The decomposition is used to discuss properties of the spectrum and the eigenspaces of the Dirac operator.
- OSTI ID:
- 21013789
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 48; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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