Harmonic spinors on homogeneous spaces

Details Harmonic spinors on homogeneous spaces Harmonic spinors on homogeneous spaces

2000-05-05

arxiv.org/abs/math/0005056v1

Represent. Theory 4 (2000) 466-473

Mathematics

Differential Geometry

7 pages

Scientific paper

Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of H. Here, we give a quick proof of this result, computing the index and kernel of this twisted Dirac operator using a homogeneous version of the Weyl character formula noted by Gross, Kostant, Ramond, and Sternberg, as well as recent work of Kostant regarding an algebraic version of this Dirac operator.

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