Equivariant indices of Spin$^c$-Dirac operators for proper moment maps

@article{Hochs2015EquivariantIO,
  title={Equivariant indices of Spin\$^c\$-Dirac operators for proper moment maps},
  author={P. Hochs and Y. Song},
  journal={arXiv: Differential Geometry},
  year={2015}
}
We define an equivariant index of Spin$^c$-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to the quantisation commutes with reduction principle. 
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