On the Vergne conjecture

Published 8 Sep 2015 in math.SG, math.DG, and math.RT | (1509.02425v1)

Abstract: Consider a Hamiltonian action by a compact Lie group on a possibly noncompact symplectic manifold. We give a short proof of a geometric formula for decomposition into irreducible representations of the equivariant index of a Spin$^c$-Dirac operator in this context. This formula was conjectured by Mich`ele Vergne in 2006 and proved by Ma and Zhang in 2014.

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