The equivariant Riemann-Roch theorem and the graded Todd class

Michele Vergne

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arXiv · 1612.04651

The equivariant Riemann-Roch theorem and the graded Todd class

Michele Vergne

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Abstract

Let G be a torus and M a G-Hamiltonian manifold with Kostant line bundle L and proper moment map. Let P be the weight lattice of G. We consider a parameter k and the multiplicity $m(\lambda,k)$ of the quantized representation associated to M and the k-th power of L . We prove that the weighted sum $\sum m(\lambda,k) f(\lambda/k)$ of the value of a test function f on points of the lattice $P/k$ has an asymptotic development in terms of the twisted Duistermaat-Heckman distributions associated to the graded Todd class of M. When M is compact, and f polynomial, the asymptotic series is finite and exact.

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Michele Vergne. 2016-12-14. The equivariant Riemann-Roch theorem and the graded Todd class. https://arxiv.org/abs/1612.04651

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