Integration over the quantum diagonal subgroup and associated Fourier-like algebras

By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group $\mathbb{G}$ a completely contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a deformed Fourier algebra of $\mathbb{G}$. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and So{\l}tan, the corresponding integration represented by a certain idempotent state on $C(\mathbb{G})$ makes sense as long as $\mathbb{G}$ is of Kac type. Finally we analyse as an explicit example the algebras $A_\Delta(O_N^+)$, $N\ge 2$, associated to Wang's free orthogonal groups, and show that they are not operator weakly amenable.Comment: Minor updates; Remark 5.7 has been added; 31 page

A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries

Let $G$ be a co-amenable compact quantum group. We show that a right coideal of $G$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on $SU_q(N)$ for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.Comment: 28 pages, Remark 4.9 adde

The nature of the unresolved extragalactic soft CXB

In this paper we investigate the power spectrum of the unresolved 0.5-2 keV CXB with deep Chandra 4 Ms observations in the CDFS. We measured a signal which, on scales >30", is significantly higher than the Shot-Noise and is increasing with the angular scale. We interpreted this signal as the joint contribution of clustered undetected sources like AGN, Galaxies and Inter-Galactic-Medium (IGM). The power of unresolved cosmic sources fluctuations accounts for \sim 12% of the 0.5-2 keV extragalactic CXB. Overall, our modeling predicts that \sim 20% of the unresolved CXB flux is made by low luminosity AGN, \sim 25% by galaxies and \sim 55% by the IGM (Inter Galactic Medium). We do not find any direct evidence of the so called Warm Hot Intergalactic Medium (i.e. matter with 10^5K<T<10^7K and density contrast {\delta} <1000), but we estimated that it could produce about 1/7 of the unresolved CXB. We placed an upper limit to the space density of postulated X-ray-emitting early black hole at z>7.5 and compared it with SMBH evolution models.Comment: 15 pages, 9 figures, accepted by MNRA

On the cosmic evolution of the scaling relations between black holes and their host galaxies: Broad Line AGN in the zCOSMOS survey

(Abriged) We report on the measurement of the rest frame K-band luminosity and total stellar mass of the hosts of 89 broad line Active Galactic Nuclei detected in the zCOSMOS survey in the redshift range 1<z<2.2. The unprecedented multiwavelength coverage of the survey field allows us to disentangle the emission of the host galaxy from that of the nuclear black hole in their Spectral Energy Distributions. We derive an estimate of black hole masses through the analysis of the broad Mg II emission lines observed in the medium-resolution spectra taken with VIMOS/VLT as part of the zCOSMOS project. We found that, as compared to the local value, the average black hole to host galaxy mass ratio appears to evolve positively with redshift, with a best fit evolution of the form (1+z)^{0.68 \pm0.12 +0.6 -0.3}, where the large asymmetric systematic errors stem from the uncertainties in the choice of IMF, in the calibration of the virial relation used to estimate BH masses and in the mean QSO SED adopted. A thorough analysis of observational biases induced by intrinsic scatter in the scaling relations reinforces the conclusion that an evolution of the MBH-M* relation must ensue for actively growing black holes at early times: either its overall normalization, or its intrinsic scatter (or both) appear to increase with redshift. This can be interpreted as signature of either a more rapid growth of supermassive black holes at high redshift, a change of structural properties of AGN hosts at earlier times, or a significant mismatch between the typical growth times of nuclear black holes and host galaxies.Comment: 47 pages, 8 figures. Accepted for publication in Ap

A new measurement of the cosmic X-ray background

We present a new measurement of the cosmic X-ray background (CXRB) in the 1.5-7 keV energy band, performed by exploiting the Swift X-ray telescope (XRT) data archive. We also present a CXRB spectral model in a wider energy band (1.5-200 keV), obtained by combining these data with the recently published Swift-BAT measurement. From the XRT archive we collect a complete sample of 126 high Galactic latitude gamma-ray burst (GRB) follow-up observations. This provides a total exposure of 7.5 Ms and a sky-coverage of 7 square degrees which represents a serendipitous survey, well suited for a direct measurement of the CXRB in the 1.5-10 keV interval. Our work is based on a complete characterization of the instrumental background and an accurate measurement of the stray-light contamination and vignetting calibration. We find that the CXRB spectrum in the 1.5-7 keV energy band can be equally well fitted by a single power-law with photon index Gamma=1.47+/-0.07 or a single power-law with photon index Gamma=1.41+/-0.06 and an exponential roll-off at 41 keV. The measured flux in the 2-10 keV energy band is 2.18+/-0.13 E-11 erg/(cm2 s deg2) in the 2-10 keV band. Combining Swift-XRT with Swift-BAT (15-200 keV) we find that, in the 1.5-200 keV band, the CXRB spectrum can be well described by two smoothly-joined power laws with the energy break at 29.0+/-0.5 keV corresponding to a nu F_nu peak located at 22.4+/-0.4 keV. Taking advantage of both the Swift high energy instruments (XRT and BAT), we produce an analytical description of the CXRB spectrum over a wide (1.5-200 keV) energy band. This model is marginally consistent with the HEAO1 measurement (~10% higher at energies higher than 20 keV, while it is significantly (30%) higher at low energies (2-10 keV).Comment: Accepted for publication by A&A; 9 pages, 11 figures. Typo corrected in units of Tab. 2; update Fig. 1