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In this article we give formulae for the Riemann–Roch number of a symplectic quotient arising as the reduced space of a coadjoint orbit OΛ (for Λ∈g* close to 0) as an evaluation of cohomology classes over the reduced space at 0. Such a formula exhibits the dependence of the Riemann–Roch number on Λ. We also express the formula as a sum over the components of the fixed point set of the maximal toru...

Symplectic fibrations and Riemann–Roch numbers of reduced spaces