On Taylor and other joint spectra for commuting n-tuples of operators

AbstractLet R and S be commuting n-tuples of operators. We will give some spectral relations between RS and SR that extend the case of single operators. We connect the Taylor spectrum, the Fredholm spectrum and some other joint spectra of RS and SR. Applications to Aluthge transforms of commuting n-tuples are also provided

Twisted Moduli Spaces and Duistermaat-Heckman Measures

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.Comment: 37 pages, 4 figures, 1 tabl