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arXiv · 2007.00103

Twisted Moduli Spaces and Duistermaat-Heckman Measures

Ahmed J. Zerouali
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Abstract

Following Boalch-Yamakawa and Meinrenken, we consider a certain class of moduli spaces on bordered surfaces from a quasi-Hamiltonian perspective. For a given Lie group $G$, these character varieties parametrize flat $G$-connections on "twisted" local systems, in the sense that the transition functions take values in $G\rtimes\mathrm{Aut}(G)$. After reviewing the necessary tools to discuss twisted quasi-Hamiltonian manifolds, we construct a Duistermaat-Heckman (DH) measure on $G$ that is invariant under the twisted conjugation action $g\mapsto hg\kappa(h^{-1})$ for $\kappa\in\mathrm{Aut}(G)$, and characterize it by giving a localization formula for its Fourier coefficients. We then illustrate our results by determining the DH measures of our twisted moduli spaces.

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BibTeXRIS

Ahmed J. Zerouali. 2020-06-30. Twisted Moduli Spaces and Duistermaat-Heckman Measures. https://doi.org/10.1016/j.geomphys.2020.104042

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