Sharing quantum nonlocality in star network scenarios

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions.In recent years,the sharing ability of the Bell nonlocality has been extensively studied.The nonlocality of quantum network states is more complex.We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements,and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability,but different under bilateral measurements.For the star network scenarios,we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states,for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.

Capelli identity on multiparameter quantum linear groups

A quantum Capelli identity is given on the multiparameter quantum general linear group based on the(p_(ij),u)-condition. The multiparameter quantum Pfaffian of the(p_(ij), u)-quantum group is also introduced and the transformation under the congruent action is given. Generalization to the multiparameter hyper-Pfaffian and relationship with the quantum minors are also investigated.

Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation

Let g be a(twisted or untwisted)affine Kac-Moody algebra,and μ be a diagram automorphism of g.In this paper,we give an explicit realization for the universal central extensionˆg[μ]of the twisted loop algebra of g with respect toμ,which provides a Moody-Rao-Yokonuma presentation for the algebraˆg[μ]whenμis non-transitive,and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.

Generalized McKay Quivers of Rank Three

For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 （C） are explicitly described and classified based on representation theory.

R-Matrix Realization of Two-Parameter Quantum Group Ur,s(gln)

We provide a Faddeev–Reshetikhin–Takhtajan’sRTT approach to the quantum group Fun(GLr,s(n))and the quantum enveloping algebra Ur,s(gln)corresponding to the two-parameter R-matrix.We prove that the quantum determinant detr,sT is a quasi-central element in Fun(GLr,s(n))generalizing earlier results of Dipper–Donkin and Du–Parshall–Wang.The explicit formulation provides an interpretation of the deforming parameters,and the quantized algebra Ur,s(R)is identified to Ur,s(gln)as the dual algebra.We then construct n−1 quasi-central elements in Ur,s(R)which are analogs of higher Casimir elements in Uq(gln).

Vertex Representations of Toroidal Special Linear Lie Superalgebras

Based on the loop-algebraic presentation of 2-toroidal Lie superalgebras, a free field representation of toroidal Lie superalgebras of type A(m, n) is constructed using both vertex operators and bosonic fields.

Modules for double affine Lie algebras

在为两倍仿射的谎言代数学的水平零点的想象的 Verma 模块，寓言的想象的 Verma 模块，和 Verma 模块用三不同三角形的分解被构造。他们的关系被调查，并且几结果从仿射的谎言代数学被概括。特别地，想象的最高的重量模块， integrable 模块，和 irreducibility 标准也被学习。

Tau functions of the charged free bosons

We study bosonic tau functions in relation with the charged free bosonic fields.It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector,and some tau functions are given in the completion M by using Schur functions.We also give a new proof of Borchardt’s identity and obtain several q-series identities by using the boson-boson correspondence.

Level-1/2 Realization of Quantum N-Toroidal Algebra in Type C_(n)

We construct a level-1/2 vertex representation of the quantum N-toroidal algebra of type C_(n),which is a natural generalization of the usual quantum toroidal algebra.The construction also provides a vertex representation of the quantum toroidal algebra for type C_(n) as a by-product.

从Frobenius特征标公式到顶点算子

本文利用群表示论方法简洁证明了Frobenius对称群特征标公式和Specht圈群特征标公式. Frobenius关于对称群的特征标公式已经显现了顶点算子的雏形,本文提出的证明关键是利用对称群Grothendieck环的乘法公式得到Bernstein顶点算子.同时,本文将此方法推广到圈群链的Grothendieck环,利用顶点算子和广义Clifford代数导出圈群的不可约特征标,简单地证明了Specht关于圈群的特征标公式.

Uncertainty relations based on Wigner-Yanase skew information

In this paper,we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information.First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds.We then propose new weighted uncertainty relations for two noncompatible observables.Two separable criteria via skew information are also obtained.

A twisted quantum toroidal algebra

As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space.

On multivariable Zassenhaus formula

We give a recursive algorithm to compute the multivariable Zassenhaus formula e^X1+X2+…+Xn=e^X1eX2…e^Xn∏∞k=2e^Wk and derive an effective recursion formula of Wk.