On the Vergne conjecture |
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Authors: | Peter Hochs Yanli Song |
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Affiliation: | 1.University of Adelaide,Adelaide,Australia;2.Dartmouth College,Hanover,USA |
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Abstract: | Consider a Hamiltonian action by a compact Lie group on a possibly non-compact symplectic manifold. We give a short proof of a geometric formula for the decomposition into irreducible representations of the equivariant index of a ({{mathrm{{{mathrm{Spin}}}^c}}})-Dirac operator in this context. This formula was conjectured by Vergne in (Eur Math Soc Zürich I:635–664, 2007) and proved by Ma and Zhang in (Acta Math 212:11–57, 2014). |
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