Quantum affine algebras and universal R-matrix with spectral parameter, II

This paper is an extended version of our previous short letter \cite{ZG2} and is attempted to give a detailed account for the results presented in that paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra and $U_q({\cal G})$ be the corresponding quantum simple Lie algebra. Using the previous obtained universal $R$-matrix for $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for $U_q(A_1)$ and $U_q(A_2)$. We apply these spectral-dependent universal $R$-matrix to some concrete representations. We then reproduce the well-known results for the fundamental representations and we are also able to derive for the first time the extreamly explicit and compact formula of the spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the simplest nontrival case when the tensor product of the representations is {\em not} multiplicity-free.Comment: 22 page

Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

We introduce the quasi-Hopf superalgebras which are $Z_2$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is the face type $B_{q,\lambda}(G)$ and the vertex type $A_{q,p}[\hat{sl(n|n)}]$ (and $A_{q,p}[\hat{gl(n|n)}]$), where $G$ is any Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for $U_q[\hat{sl(n|n)}]$ in a non-standard system of simple roots, all of which are fermionic.Comment: 22 pages, Latex fil

Long-Range Coulomb Effect on the Antiferromagnetism in Electron-doped Cuprates

Using mean-field theory, we illustrate the long-range Coulomb effect on the antiferromagnetism in the electron-doped cuprates. Because of the Coulomb exchange effect, the magnitude of the effective next nearest neighbor hopping parameter increases appreciably with increasing the electron doping concentration, raising the frustration to the antiferromagnetic ordering. The Fermi surface evolution in the electron-doped cuprate Nd$_{2-x}$Ce$_x$CuO$_4$ and the doping dependence of the onset temperature of the antiferromagnetic pseudogap can be reasonably explained by the present consideration.Comment: 4 pages, 4 figure

Timely Updates over an Erasure Channel

Using an age of information (AoI) metric, we examine the transmission of coded updates through a binary erasure channel to a monitor/receiver. We start by deriving the average status update age of an infinite incremental redundancy (IIR) system in which the transmission of a k-symbol update continuesuntil k symbols are received. This system is then compared to a fixed redundancy (FR) system in which each update is transmitted as an n symbol packet and the packet is successfully received if and only if at least k symbols are received. If fewer than k symbols are received, the update is discarded. Unlike the IIR system, the FR system requires no feedback from the receiver. For a single monitor system, we show that tuning the redundancy to the symbol erasure rate enables the FR system to perform as well as the IIR system. As the number of monitors is increased, the FR system outperforms the IIR system that guarantees delivery of all updates to all monitors