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Symplectic fibrations and Riemann-Roch numbers of reduced spaces

Mark Hamilton·Lisa Jeffrey
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Abstract

In this article we give formulas for the Riemann-Roch number of a symplectic quotient arising as the reduced space corresponding to a coadjoint orbit (for an orbit close to 0) as an evaluation of cohomology classes over the reduced space at 0. This formula exhibits the dependence of the Riemann-Roch number on the Lie algebra variable which specifies the orbit. We also express the formula as a sum over the components of the fixed point set of the maximal torus. Our proof applies to Hamiltonian G-manifolds even if they do not have a compatible Kahler structure, using the definition of quantisation in terms of the Spin-C Dirac operator.

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Mark Hamilton, Lisa Jeffrey. 2005-01-04. Symplectic fibrations and Riemann-Roch numbers of reduced spaces. https://arxiv.org/abs/math/0403004

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