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- W2895194414 abstract "We prove a Fredholm property for spin-c Dirac operators $$mathsf {D}$$ on non-compact manifolds satisfying a certain condition with respect to the action of a semi-direct product group $$Kltimes Gamma $$ , with K compact and $$Gamma $$ discrete. We apply this result to an example coming from the theory of Hamiltonian loop group spaces. In this context we prove that a certain index pairing $$[{mathcal {X}}] cap [mathsf {D}]$$ yields an element of the formal completion $$R^{-infty }(T)$$ of the representation ring of a maximal torus $$T subset H$$ ; the resulting element has an additional antisymmetry property under the action of the affine Weyl group, indicating $$[{mathcal {X}}] cap [mathsf {D}]$$ corresponds to an element of the ring of projective positive energy representations of the loop group." @default.
- W2895194414 created "2018-10-12" @default.
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- W2895194414 date "2018-11-01" @default.
- W2895194414 modified "2023-10-17" @default.
- W2895194414 title "Quantization of Hamiltonian loop group spaces" @default.
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- W2895194414 doi "https://doi.org/10.1007/s00208-018-1771-z" @default.
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