Uq(sl(2))的二维循环表示,C—G系数和一个自由费米子八顶角模型

明确地构造了量子代数U_q(Sl(2))当q=i和z中心扩张时的两维循环表示,此表示是既约的;给出了张量表示的C—G规则和C—G系数以及不同次序张量表示的扭结子(Intertwiner).此扭结子是一个满足自由费米子条件的八顶角R矩阵,因此给出了一个可积顶角模型.     

SO5 SU2 SU2 U1 U1及SO5 U1 U1的矢量相干态表示

本文讨论了SO₅ SU₂ SU₂ U₁ U₁及SO₅ U₁ U₁的VCS表示.计算了SO₅ U₂ U₂的约化矩阵元,并利用K矩阵技术确定了SO₅权的多重度.     

量子群GL(3)q的Verma模,q-boson实现和Cyclic表示

本文利用类似研究半单李代数的结构和Verma模的方法研究了量子群GL(3)_q的矩阵元代数A(3)_q的结构和Verma模.然后利用A(3)_q的Verma表示构造了A(3)_q的q-boson实现,并借助于此实现研究了当q^p≡1时的A(3)_q的Cyclic表示.     

SU3 U1 U1的矢量相干态表示

本文讨论了U₃的矢量相干态表示.利用K矩阵技术得到了SU₃ U₁ U₁的正交基矢,从而确定了权的多重度.     

利用SU(2)q,s量子代数的两参数变形振子实现讨论SU(2)q,s相干态

利用SU(2)_q,s量子代数的两参数变形振子实现构造出与Perelomov相干态形式不同的SU(2)_q,s相干态.证明了SU(2)_q,s量子代数的表示基是正交的,并讨论了它的相干态的归一性和完备性.指出SU(2)_q,s相干态的相干性受参数q,s的影响,它比单参数变形SU(2)_q相干态更具一般性.     

量子代数SUq(4)的不可约表示

本文利用类张量的方法计算了量子代数SU_q(4)在SU_q(4)>SU_q(2)+SU_q(2)基上的不可约表示,得到了求矩阵元的递推公式.     

量子Lie超代数SLq(2/1)的不可约表示

本文指出满足Serre关系的某些SL_q(2/1)的生成元,可以认作是SL_q(2)的1/2阶张量算符,它们的约化矩阵可以通过一组递推公式算出.因此,SL_q(2/1)的不可约表示可以完全被决定.     

核转动谱的量子群SUq(2)理论分析

本文系统地分析了量子群SU_q(2)理论对原子核转动谱的适用性.通过对Mallmann图、I(I+1)展开系数的关系、以及能谱的计算表明:SU_q(2)的转动谱表示式与锕系和稀土偶偶变形核的观测到的转动谱规律有明显的偏离.SU_q(2)转动谱表示式只在一定角动量范围中适用.形变参量q与核软度直接相关,明显依赖于角动量.     

具有Uqp(U3)Uqp)(U2) Uqp(SO2)对称的双参数形变二维相互作用玻色子模型

构造了具有U_qp(U₃) U_qp(U₂) U_qp(SO₂)对称的双参数qp-形变二维相互作用玻色子模型(IBM),并给出了其能谱和跃迁矩阵元.结果表明,能谱和跃迁矩阵元极其敏感地依赖于第二个形变参数.     

Bi2WO6光催化剂的γ射线辐射效应

本文首次研究了高能辐射(γ射线)对Bi₂WO₆纳米晶体结构和光催化性能的影响. 结果表明,尽管高能辐射不会改变Bi₂WO₆纳米晶体的形貌,但是Bi₂WO₆粉末的颜色在高吸收剂量辐照(507 kGy)后发生了明显的变化,并且辐照后Bi₂WO₆的XRD谱图也显示,随着吸收剂量的增加,(113)晶面对应的2θ从28.37°移到28.45°,说明晶格参数在γ射线辐照下还是发生了细微的变化. XPS表征结果证明,Bi₂WO₆晶体结构的变化源于高剂量辐射下氧空位缺陷的产生. Bi₂WO₆纳米晶体的禁带宽度(E_g)随吸收剂量的增加也出现减小的趋势. 用水溶液中亚甲基蓝的可见光照分解反应作为模型反应考察了辐照后的Bi₂WO₆纳米晶体的光催化活性,结果表明,辐照后的Bi₂WO₆纳米晶体的光催化活性随着吸收剂量的增加而逐渐升高. 将经过反应后的Bi₂WO₆纳米晶体再次回收,进行循环催化,发现这些辐照后的Bi₂WO₆纳米晶体在三次循环使用后光催化性能仍然能够保持,说明高能辐射产生的氧空位缺陷具有良好的稳定性.     

Two Dimensional Cyclic Representations of Uq(sl2)and 8-Vertex Ising Model

We give explicitly the 2-dimensional cyclic representations of quantum algebra U_q(sl₂)with central extension.The intertwiner for tensor representations in different ordersis constructed with C-G coefficients.This intertwiner is shown to be the R -matrix for eight vertex Ising model.     

U_q（sl（2））的二维循环表示，C—G系数和一个自由费米子八顶角模型

明确地构造了量子代数Ｕｑ（Ｓｌ（２））当ｑ＝ｉ和ｚ中心扩张时的两维循环表示，此表示是既约的；给出了张量表示的Ｃ—Ｇ规则和Ｃ—Ｇ系数以及不同次序张量表示的扭结子（Ｉｎｔｅｒｔｗｉｎｅｒ）．此扭结子是一个满足自由费米子条件的八顶角Ｒ矩阵，因此给出了一个可积顶角模型．     

Classical intertwiner space and quantization

Given two symplectic realizations, a symplectic manifold called the classical intertwiner space is introduced as a classical analogue of an intertwiner space of representations of an associative algebra. We describe explicitly how a quantum data on realizations induces a quantum data on their classical intertwiner space.Research partially supported by NSF Grant DMS92-03398 and at MSRI supported by NSF Grant DMS90-22140     

Etiology of IRF models

We show that a class of 2D statistical mechanics models known as IRF models can be viewed as a subalgebra of the operator algebra of vertex models. Extending the Wigner calculus to quantum groups, we obtain an explicit intertwiner between two representations of this subalgebra.     

Dyonic Sectors and Intertwiner Connections in 2+1-Dimensional Lattice -Higgs Models

We construct dyonic states in 2+1-dimensional lattice -Higgs models, i.e. states which are both, electrically and magnetically charged. These states are parametrized by , where ɛ and μ are -valued electric and magnetic charge distributions, respectively, living on the spatial lattice . The associated Hilbert spaces carry charged representations of the observable algebra , the global transfer matrix t and a unitary implementation of the group of spatial lattice translations. We prove that for coinciding total charges these representations are dynamically equivalent and we construct a local intertwiner connection , where is a path in the space of charge distributions . The holonomy of this connection is given by -valued phases. This will be the starting point for a construction of scattering states with anyon statistics in a subsequent paper. Received: 13 December 1996 / Accepted: 19 May 1997     

Entanglement in simple spin networks with a boundary

We investigate the bipartite entanglement for the boundary states in a simple type of spin networks with dangling edges, in which the two complementary parts are linked by two or more edges. Firstly, the spin entanglement is considered in the absence of the intertwiner entanglement. By virtue of numerical simulations, we find that the entanglement entropy usually depends on the group elements. More importantly, when the intertwiner entanglement is taken into account, we find that it is in general impossible to separate the total entanglement entropy into the contribution from spins on edges and the contribution from intertwiners at vertices. These situations are in contrast to the case when the two vertices are linked by a single edge.     

Algebraic Bethe ansatz for the eight-vertex model with general open boundary conditions

By using the intertwiner and face-vertex correspondence relation, we obtain the Bethe ansatz equation of the eight-vertex model with open boundary conditions in the framework of algebraic Bethe ansatz method. The open boundary condition under consideration is the general solution of the reflection equation for the eight-vertex model with only one restriction on the free parameters of the right side reflecting boundary matrix. The reflecting boundary matrices used in this paper thus may have off-diagonal elements. Our construction can also be used for the Bethe ansatz of SOS model with reflection boundaries.     

On the integrability of the SU(N) Hubbard model

We exhibit explicitly the intertwiner operator for the monodromy matrices of the SU(N) Hubbard model recently proposed by Maassarani [Phys. Lett. A 239 (1998) 187]. This produces a new family of non-additive R-matrices and generalizes an earlier result by Shastry [Phys. Rev. Lett. 56 (1986) 2453; J. Stat. Phys. 30 (1988) 57].     

Deformation Quantizations of the Poisson Algebra of Laurent Polynomials

It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space R2n up to equivalence. In his presentation of an interesting deformation quantization of the Poisson algebra of Laurent polynomials, Ovsienko discusses the equivalences of deformation quantizations of these algebras. We show that under suitable conditions, deformation quantizations of this algebra are equivalent. Though Ovsienko showed that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product, this is not correct. We show this equivalence by two methods: a direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild 2-cocycles.     

An ?-Deformed Virasoro Algebra as Hidden Symmetry of the Restricted sine-Gordon Model

As the Yangian double with center, which is deformed from affine algebra by the additive loop parameter ?, we get the commutation relation and the bosonization of quantum ?-deformed Virasoro algebra. The corresponding Miura transformation, the associated screening operators and the BRST charge have been studied. Moreover, we also construct the bosonization for type Ⅰ and type Ⅱ intertwiner vertex operators. Finally, we show that the commutation relations of these vertex operators in the case of p^′ = γ, p = γ - 1 and ? = π actually give the exact scattering matrix of the restricted sine-Gordon model.