Geometry and Representations of the Quantum Supergroup OSPq(1|2n)

The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter - Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes' theory. Parabolic induction is developed by employing the quantum homogeneous supervector bundles. Quantum Frobenius reciprocity and a generalized Borel - Weil theorem are established for the induced representations.Comment: Latex, 20 page

Observation of Terahertz Radiation via the Two-Color Laser Scheme with Uncommon Frequency Ratios

In the widely-studied two-color laser scheme for terahertz (THz) radiation from a gas, the frequency ratio of the two lasers is usually fixed at $\omega_2/\omega_1=$1:2. We investigate THz generation with uncommon frequency ratios. Our experiments show, for the first time, efficient THz generation with new ratios of $\omega_2/\omega_1=$1:4 and 2:3. We observe that the THz polarization can be adjusted by rotating the longer-wavelength laser polarization and the polarization adjustment becomes inefficient by rotating the other laser polarization; the THz energy shows similar scaling laws with different frequency ratios. These observations are inconsistent with multi-wave mixing theory, but support the gas-ionization model. This study pushes the development of the two-color scheme and provides a new dimension to explore the long-standing problem of the THz generation mechanism.Comment: 6 pages, 3 figure

On Gorenstein Surfaces Dominated by P^2

In this paper we prove that a normal Gorenstein surface dominated by the projective plane P^2 is isomorphic to a quotient P^2/G, where G is a finite group of automorphisms of P^2 (except possibly for one surface V_8'). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.Comment: Nagoya Mathematical Journal, to appea

The Protocluster G18.67+0.03: A Test Case for Class I Methanol Masers as Evolutionary Indicators for Massive Star Formation

We present high angular resolution Submillimeter Array (SMA) and Karl G. Jansky Very Large Array (VLA) observations of the massive protocluster G18.67+0.03. Previously targeted in maser surveys of GLIMPSE Extended Green Objects (EGOs), this cluster contains three Class I methanol maser sources, providing a unique opportunity to test the proposed role of Class I masers as evolutionary indicators for massive star formation. The millimeter observations reveal bipolar molecular outflows, traced by 13CO(2-1) emission, associated with all three Class I maser sources. Two of these sources (including the EGO) are also associated with 6.7 GHz Class II methanol masers; the Class II masers are coincident with millimeter continuum cores that exhibit hot core line emission and drive active outflows, as indicated by the detection of SiO(5-4). In these cases, the Class I masers are coincident with outflow lobes, and appear as clear cases of excitation by active outflows. In contrast, the third Class I source is associated with an ultracompact HII region, and not with Class II masers. The lack of SiO emission suggests the 13CO outflow is a relic, consistent with its longer dynamical timescale. Our data show that massive young stellar objects associated only with Class I masers are not necessarily young, and provide the first unambiguous evidence that Class I masers may be excited by both young (hot core) and older (UC HII) MYSOs within the same protocluster.Comment: Astrophysical Journal Letters, accepted. emulateapj, 7 pages including 4 figures and 1 table. Figures compressed. v2: coauthor affiliation updated, emulateapj versio

Optical detection of a BCS phase transition in a trapped gas of fermionic atoms

Light scattering from a spin-polarized degenerate Fermi gas of trapped ultracold Li-6 atoms is studied. We find that the scattered light contains information which directly reflects the quantum pair correlation due to the formation of atomic Cooper pairs resulting from a BCS phase transition to a superfluid state. Evidence for pairing can be observed in both the space and time domains.Comment: 8 pages, 4 figures, revte