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Finite dimensional modules over quantum toroidal algebras

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Frontiers of Mathematics in China 2020年第3期15卷 593-600页

作者： limeng XIA Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013China

For all generic q∈C^∗,when g is not of type A1;we prove that the quantum toroidal algebra Uq(gtor)has no nontrivial finite dimensional simple module.

关键词： Quantum toroidal algebra finite dimensional module

STEP-LIKE CONTRAST STRUCTURE OF SINGULARLY PERTURBED OPTIMAL CONTROL PROBLEM＊

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Journal of Computational Mathematics 2012年第1期30卷 2-13页

作者： Mingkang Ni limeng Wu Department of Mathematics East China Normal UniversityShanghai 200241China

The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. As an application, an example is given to illustrate the main result in this paper.

关键词： Singular perturbation Optimal control problem Contrast structure.

Classification on irreducible Whittaker modules over quantum group Uq(sl3,∧)

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Frontiers of Mathematics in China 2021年第4期16卷 1089-1097页

作者： limeng XIA Xiangqian GUO Jiao ZHANG Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013China School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China Department of Mathematics Shanghai UniversityShanghai 200444China

We define the Whittaker modules over the simply-connected quantum group U_(q)(sl3,∧),where A is the weight lattice of Lie algebra *** we completely classify all those simple ***,a simple Whittaker module over U_(q)(sl3,∧)is either a highest weight module,or determined by two parameters z∈C andγ∈C^(*)(up to a Hopf automorphism).

关键词： Quantum group simple Whittaker module Whittaker vector

Twisted Whittaker modules over U_(q)(gl_(n+1))

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Science China Mathematics 2023年第10期66卷 2191-2202页

作者： limeng Xia Kaiming Zhao Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013China Department of Mathematics Wilfrid Laurier UniversityWaterlooON N2L 3C5Canada School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024China

As is well known,the classical nonsingular Whittaker modules over quantum groups cannot be defined for the non-A1 *** this paper,by choosing different generators for the quantum group U_(q)(gl_(n+1)),we introduce and study the twisted Whittaker modules over U_(q)(gl_(n+1)).We classify all the simple twisted Whittaker modules with nonsingular Whittaker *** agrees with Kostant’s results on Whittaker modules for the simple complex Lie algebras sln+1 as q approaches 1.

关键词： quantum group center Whittaker module

Majid conjecture: quantum Kac-Moody algebras version

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Frontiers of Mathematics in China 2021年第3期16卷 727-747页

作者： Hongmei HU Naihong HU limeng XIA School of Mathematical Sciences Suzhou University of Science and TechnologyShihu CampusSuzhou215009China School of Mathematical Sciences Shanghai Key Laboratory of PMMPEast China Normal UniversityMinhang CampusShanghai200241China Institute of Applied System Analysis Jiangsu UniversityZhenjiang212013China

Based on the n-fold tensor product version of the generalized double-bosonization construction,we prove the Majid conjecture of the quantum Kac-Moody algebras ***,we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G(1)2,E(1)6,and Tp,q,r,and in this way,we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor *** gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.

关键词： Double-bosonization quantum Kac-Moody algebras R-matrix

A QUANTITATIVE MODEL FOR INTRADAY STOCK PRICE CHANGES BASED ON ORDER FLOWS

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Journal of Systems Science & Complexity 2014年第1期27卷 208-224页

作者： limeng HUI Xiaofeng ENDO Misao KISHIMOTO Kazuo School of Management Harbin Institute of Technology Harbin 150001 China. Socio-economic Research Center Central Research Institute of Electric Power Industry Tokyo 100-8126 Japan. Graduate School of Systems Information Engineering University of Tsukuba Ibaraki-ken 305-8571 Japan.

This paper proposes a double Markov model of the double continuous auction for describing intra-day price changes. The model splits intra-day price changes as the repetition of one tick price moves and assumes order arrivals are independent Poisson random processes. The dynamic process of price formation is described by a birth-death process of the double M/M/1 server queue corresponding to the best bid/ask. The initial depths of the best bid and ask are defined as different constants depending on the last price change. Thus, the price changes in the model follow a first-order Markov process. As the initial depth of the best bid/ask is originally larger than that of the opposite side when the last price is down/up, the model may explain the negative autocorrelations of the price of the best bid/ask. The estimated parameters are based on the real tick-by-tick data of the Nikkei 225 futures listed in Osaka Stock Exchanges. The authors find the model accurately predicts the returns of Osaka Stock Exchange average.

关键词： Intra-day price changes market microstructure order flow queuing theory.

The Polynomial Modules over Quantum Group U_(q)(sl3)

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Algebra Colloquium 2022年第4期29卷 663-668页

作者： limeng Xia Qianqian Cai Jiao Zhang Institute of Applied System Analysis Jiangsu University ZhenjiangJiangsu 212013China Department of Mathematics Shanghai UniversityShanghai 200444China

Let g be a finite dimensional complex simple Lie algebra with Cartan subalgebraη.Then C[η]has a g-module structure if and only if g is of type A or of type C;this is called the polynomial module of rank one,In the quantum version,the rank one polynomial modules over U_(q)(sl_(2))have been *** this paper,we prove that the quantum group U_(q)(sl_(3))has no rank one polynomial module.

关键词： quantum group polynomial module rank one

On the centers of quantum groups of A_n-type

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Science China Mathematics 2018年第2期61卷 287-294页

作者： Libin Li limeng Xia Yinhuo Zhang College of Mathematical Science Yangzhou University Institute of Applied System Analysis Jiangsu University Department of Mathematics and Statistics University of HasseltUniversitaire Campus

Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).

关键词： center quantum group type An Casimir element

Probabilistic Optimal Power Flow of an AC/DC System with a Multiport Current Flow Controller

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CSEE Journal of Power and Energy Systems 2021年第4期7卷 744-752页

作者： Jing Bian He Wang limeng Wang Guoqing Li Zhenhao Wang Department of Electrical Engineering Northeast Electric Power UniversityJilin 132000China

To evaluate the impact of the randomness and correlation of photovoltaic(PV)and load on AC/DC systems with a multiport current flow controller(M-CFC),this paper proposes a probabilistic optimal power flow calculation for AC/DC systems,based on a nonparametric kernel density ***,according to the M-CFC model,the DC power flow calculation method with M-CFC was inferred,and its influence on line loss was ***,a nonparametric kernel density estimation with an adaptive bandwidth is used to accurately describe the probability distribution of the PV and load,and correlation samples of the PV and load are obtained by the mixed copula *** an optimization model that considers system loss and static security is established,and a fast nondominated sorting genetic algorithm based on the elite strategy(NSGA-II)is used to calculate the multi-objective probability optimal power flow of the AC/DC ***,a case study is performed on a modified IEEE39 bus system using measured PV and load *** verified that the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty,and M-CFC can improve the static security of the system.

关键词： AC/DC system correlation multiport current controller probabilistic optimal power flow PV