Lifting representations of finite reductive groups II: Explicit conorms

Let $k$ be a field, $\tilde{G}$ a connected reductive $k$-quasisplit group, $\Gamma$ a finite group that acts on $\tilde{G}$ via $k$-automorphisms satisfying a quasi-semisimplicity condition, and $G$ the connected part of the group of $\Gamma$-fixed points of $\tilde{G}$, also assumed $k$-quasisplit. In an earlier work, the authors constructed a canonical map $\hat{\mathcal{N}}$ from the set of stable semisimple conjugacy classes in the dual $G^*(k)$ to the set of such classes in $\tilde{G}^*(k)$. We describe several situations where $\hat{\mathcal{N}}$ can be refined to an explicit function on points, or where it factors through such a function

Depth-zero base change for unramified U(2,1)

We give an explicit description of L-packets and quadratic base change for depth-zero representations of unramified unitary groups in two and three variables. We show that this base change is compatible with unrefined minimal K-types.Comment: 30 pages; uses LaTeX packages graphics (for a rotated table) and xy (for a diagram

Measurement of light mesons at RHIC by the PHENIX experiment

The PHENIX experiment at RHIC has measured a variety of light neutral mesons ($\pi^{0}$, K$_{S}^{0}$, $\eta$, $\omega$, $\eta^{\prime}$, $\phi$) via multi-particle decay channels over a wide range of transverse momentum. A review of the recent results on the production rates of light mesons in p+p and their nuclear modification factors in d+Au, Cu+Cu and Au+Au collisions at different energies is presented.Comment: 5 pages, 4 figures, talk given at Hard Probes 2008 conference in La Toja, Spain. submitted to EPJ

Finite cosmology and a CMB cold spot

The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 x 10^23 solar masses and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.Comment: 20 pages, 12 figure

Nuclear modification at sqrt{s_{NN}}=17.3 GeV, measured at NA49

Transverse momentum spectra up to 4.5 GeV/c were measured around midrapidity in Pb+Pb reactions at sqrt{s_{NN}}=17.3 GeV, for pi^{+/-}, p, pbar and K^{+/-}, by the NA49 experiment. The nuclear modification factors R_{AA}, R_{AA/pA} and R_{CP} were extracted and are compared to RHIC results at sqrt{s_{NN}}=200 GeV. The modification factor R_{AA} shows a rapid increase with transverse momentum in the covered region. The modification factor R_{CP} shows saturation well below unity in the pi^{+/-} channel. The extracted R_{CP} values follow the 200 GeV RHIC results closely in the available transverse momentum range for all particle species. For pi^{+/-} above 2.5 GeV/c transverse momentum, the measured suppression is smaller than that observed at RHIC. The nuclear modification factor R_{AA/pA} for pi^{+/-} stays well below unity.Comment: Proceedings of Quark Matter 2008 conferenc

Correction-to-scaling exponent for two-dimensional percolation

We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by Omega <= 72/91, omega = D Omega <= 3/2, and Delta_1 = nu omega <= 2, based upon Cardy's result for the critical crossing probability on an annulus. The upper bounds are consistent with many previous measurements of site percolation on square and triangular lattices, and new measurements for bond percolation presented here, suggesting this result is exact. A scaling form evidently applicable to site percolation is also found

Phonon-modulated magnetic interactions and spin Tomonaga-Luttinger liquid in the p-orbital antiferromagnet CsO2

The magnetic response of antiferromagnetic CsO2, coming from the p-orbital S=1/2 spins of anionic O2- molecules, is followed by 133Cs nuclear magnetic resonance across the structural phase transition occuring at Ts1=61 K on cooling. Above Ts1, where spins form a square magnetic lattice, we observe a huge, nonmonotonic temperature dependence of the exchange coupling originating from thermal librations of O2- molecules. Below Ts1, where antiferromagnetic spin chains are formed as a result of p-orbital ordering, we observe a spin Tomonaga-Luttinger-liquid behavior of spin dynamics. These two interesting phenomena, which provide rare simple manifestations of the coupling between spin, lattice and orbital degrees of freedom, establish CsO2 as a model system for molecular solids.Comment: 9 pages, 5 figures (with Supplemental Material), to appear in Physical Review Letter

One-dimensional quantum antiferromagnetism in the p−p-orbital CsO2_2 compound revealed by electron paramagnetic resonance

Recently it was proposed that the orbital ordering of $\pi_{x,y}^*$ molecular orbitals in the superoxide CsO$_2$ compound leads to the formation of spin-1/2 chains below the structural phase transition occuring at $T_{\rm{s1}}=61$~K on cooling. Here we report a detailed X-band electron paramagnetic resonance (EPR) study of this phase in CsO$_2$ powder. The EPR signal appears as a broad line below $T_{\rm{s1}}$, which is replaced by the antiferromagnetic resonance below the N\'{e}el temperature $T_{\rm N}=8.3$~K. The temperature dependence of the EPR linewidth between $T_{\rm{s1}}$ and $T_{\rm{N}}$ agrees with the predictions for the one-dimensional Heisenberg antiferromagnetic chain of $S=1/2$ spins in the presence of symmetric anisotropic exchange interaction. Complementary analysis of the EPR lineshape, linewidth and the signal intensity within the Tomonaga-Luttinger liquid (TLL) framework allows for a determination of the TLL exponent $K=0.48$. Present EPR data thus fully comply with the quantum antiferromagnetic state of spin-1/2 chains in the orbitally ordered phase of CsO$_2$, which is, therefore, a unique $p-$orbital system where such a state could be studied.Comment: 6 pages, 3 figure

Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1