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Symplectic reduction and a weighted multiplicity formula for twisted Spin$^c$-Dirac operators

Youliang Tian·Weiping Zhang
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Abstract

We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin$^c$-complex under consideration is allowed to be further twisted by certain natural exterior power bundles. The main result is a weighted quantization formula in the presence of commuting Hamiltonian actions. The corresponding Morse type inequalities in holomorphic situations are also established.

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Youliang Tian, Weiping Zhang. 1998-02-22. Symplectic reduction and a weighted multiplicity formula for twisted Spin$^c$-Dirac operators. https://arxiv.org/abs/math/9802105

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