Dual canonical bases for the quantum special linear group and invariant subalgebras

A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a ``canonical basis'' for every finite dimensional irreducible $U_q({\mathfrak{sl}}(n))$-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quantum minors.Comment: 15 page

Serre presentations of Lie superalgebras

An analogue of Serre's theorem is established for finite dimensional simple Lie superalgebras, which describes presentations in terms of Chevalley generators and Serre type relations relative to all possible choices of Borel subalgebras. The proof of the theorem is conceptually transparent; it also provides an alternative approach to Serre's theorem for ordinary Lie algebras.Comment: 45 page

Quantum supergroups and topological invariants of three - manifolds

The Reshetikhin - Turaeve approach to topological invariants of three - manifolds is generalized to quantum supergroups. A general method for constructing three - manifold invariants is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, $U_q(gl(2|1))$ at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.Comment: 22 page

Topological Invariants For Lens Spaces And Exceptional Quantum Groups

The Reshetikhin - Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras $G_2$, $F_4$ and $E_8$ at odd roots of unity are constructed and explicitly computed for all the lens spaces.Comment: LaTeX 10 page

Gamma Ray Burst Prompt Emission Variability in Synchrotron and Synchrotron Self-Compton Lightcurves

Gamma Ray Burst prompt emission is believed to originate from electrons accelerated in a highly relativistic outflow. "Internal shocks" due to collisions between shells ejected by the central engine is a leading candidate for electron acceleration. While synchrotron radiation is generally invoked to interpret prompt gamma-ray emission within the internal shock model, synchrotron self-Compton (SSC) is also considered as a possible candidate of radiation mechanism. In this case, one would expect a synchrotron emission component at low energies, and the naked-eye GRB 080319B has been considered as such an example. In the view that the gamma-ray lightcurve of GRB 080319B is much more variable than its optical counterpart, in this paper we study the relative variability between the synchrotron and SSC components. We develop a "top-down" formalism by using observed quantities to infer physical parameters, and subsequently to study the temporal structure of synchrotron and SSC components of a GRB. We complement the formalism with a "bottom-up" approach where the synchrotron and SSC lightcurves are calculated through a Monte-Carlo simulations of the internal shock model. Both approaches lead to the same conclusion. Small variations in the synchrotron lightcurve can be only moderately amplified in the SSC lightcurve. The SSC model therefore cannot adequately interpret the gamma-ray emission properties of GRB 080319B.Comment: 13 pages, 4 figures, accepted for publication in MNRA

A Rate-Splitting Based Bound-Approaching Transmission Scheme for the Two-User Symmetric Gaussian Interference Channel with Common Messages

This paper is concerned with a rate-splitting based transmission strategy for the two-user symmetric Gaussian interference channel that contains common messages only. Each transmitter encodes its common message into multiple layers by multiple codebooks that drawn from one separate code book, and transmits the superposition of the messages corresponding to these layers; each receiver decodes the messages from all layers of the two users successively. Two schemes are proposed for decoding order and optimal power allocation among layers respectively. With the proposed decoding order scheme, the sum-rate can be increased by rate-splitting, especially at the optimal number of rate-splitting, using average power allocation in moderate and weak interference regime. With the two proposed schemes at the receiver and the transmitter respectively, the sum-rate achieves the inner bound of HK without time-sharing. Numerical results show that the proposed optimal power allocation scheme with the proposed decoding order can achieve significant improvement of the performance over equal power allocation, and achieve the sum-rate within two bits per channel use (bits/channel use) of the sum capacity

Quark Coalescence with Quark Number Conservation and the Effect on Quark-Hadron Scaling

We develop a new formulation of the quark coalescence model by including the quark number conservation in order to describe the hadronization of the bulk of the quark-gluon plasma. The scalings between hadron and quark phase space distributions are shown to depend on the transverse momentum. For hard quarks, our general scalings reproduce the usual quadratic scaling relation for mesons and the cubic scaling relation for baryons. For softer quarks, however, the inclusion of the quark number conservation leads to a linear scaling for the hadron species that dominates the quark number of each flavor, while the scalings of non-dominant hadrons depend on the coalescence dynamics. For charm mesons, we find that the distribution of soft $D$ mesons does not depend on the light quark distribution but the distribution of soft $J/\psi$ mesons is inversely correlated to the light quark distribution.Comment: Added 6 more equations to explain the derivations; added discussions; final published versio