Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and ...Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.展开更多
In this paper,we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B,N and T,and we also compute the orders of them.Furthermore,we give explicit generat...In this paper,we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B,N and T,and we also compute the orders of them.Furthermore,we give explicit generators for the rational invariants fields of the Borel subgroup and the Neron-Severi subgroup of the general linear group.展开更多
Let F q be a finite field with qelements where q=p~α. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (n+t,n)(F q), singular unitary group U (n+...Let F q be a finite field with qelements where q=p~α. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (n+t,n)(F q), singular unitary group U (n+t,n)(F (q^2)) and singular orthogonal group O (n+t,n)(F q)(n is even) over finite fields F q.展开更多
The main purpose of this paper is to extend to classical groups a H*irmander multiplier theorem concerning translation invariant operators on L p spaces which are known for the n-torus.
The authors determine all the complete Langlands parameters corresponding to the representations of the classical groups with integral regular infintesimal characters, and get all L-packts in that case.
Let G be a classical group over an arbitrary field F,acting on an n-dimensional vector space V=V(n,F)over a field F.In this paper,we classify the maximal subgroups of G,which normalizes a solvable subgroup N of GL(L,F...Let G be a classical group over an arbitrary field F,acting on an n-dimensional vector space V=V(n,F)over a field F.In this paper,we classify the maximal subgroups of G,which normalizes a solvable subgroup N of GL(L,F)not lying in F^(*)1_(V).展开更多
Let G be a classical group over an arbitrary field F,acting on an n-dimensional F-space V=V(n,F).All those maximal subgroups of G are classified each of which normalizes a solvable subgroup N of GL(V/F)not lying in F^...Let G be a classical group over an arbitrary field F,acting on an n-dimensional F-space V=V(n,F).All those maximal subgroups of G are classified each of which normalizes a solvable subgroup N of GL(V/F)not lying in F^(*)1v.展开更多
Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cann...Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.展开更多
This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits.We de ne a(B,N)pair and construct a building out of it.Then we give a description of Chevalley groups,their(B,N)pair and...This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits.We de ne a(B,N)pair and construct a building out of it.Then we give a description of Chevalley groups,their(B,N)pair and the associated buildings.We illustrates this theory with many examples from classical groups.展开更多
This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations...This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.展开更多
The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries...The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.展开更多
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr...The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.展开更多
Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the gr...Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.展开更多
The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corre...The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.展开更多
Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the （2＋1 ）-dimensional differential Sawada Kotera （SK） equation by the classical Lie point group method, are presented...Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the （2＋1 ）-dimensional differential Sawada Kotera （SK） equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair＇s compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.展开更多
We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of sim...We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.展开更多
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equ...In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equation to some （1 ＋ 1 ）-dimensional partial differential systems. Finally, many exact travelling solutions of the （2＋1）-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.展开更多
In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmeth...In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.展开更多
Abstract homomorphisms between subgroups of algebraic groups were studied in detail by A.Borel, J.Tit.[1] and B.Wei.feile.[2] provided that the images of the homomorphisms are Zariski dense subsets and that the fields...Abstract homomorphisms between subgroups of algebraic groups were studied in detail by A.Borel, J.Tit.[1] and B.Wei.feile.[2] provided that the images of the homomorphisms are Zariski dense subsets and that the fields over which algebraic groups are defined are infinite. The purpose of this paper is to determine all embedding homomorphisms of SLn(k) into SLn(K) when k and K are any fields of the same characteristic, without assumption of Zariski density and infinitude of fields. The result in this paper generalizes a result of Chen Yu on homomorphisms of two dimensional linear groups[3].展开更多
Let F_(q)be a finite field of any characteristic and GL(n,F_(q))be the general linear group over F_(q).Suppose W denotes the standard representation of GL(n,F_(q)),and GL(n,F_(q))acts diagonally on the direct sum of W...Let F_(q)be a finite field of any characteristic and GL(n,F_(q))be the general linear group over F_(q).Suppose W denotes the standard representation of GL(n,F_(q)),and GL(n,F_(q))acts diagonally on the direct sum of W and its dual space W^(∗).Let G be any subgroup of GL(n,F_(q)).Suppose the invariant field F_(q)(W)G=F_(q)(f1,f2,…,fk),where f1,f2,…,fk in F_(q)[W]G are homogeneous invariant polynomials.We prove that there exist homogeneous polynomialsl1,l2,…,ln in the invariant ring F_(q)[W⊕W^(∗)]G such that the invariant field F_(q)(W⊕W^(∗))G is generated by{f1,f2,…,fk,l1,l2,…,ln}over F_(q).展开更多
基金Supported by the National Natural Science Foundation of China(11071081)
文摘Let D be a 2-（v, k, 4） symmetric design and G be a flag-transitive point-primitive automorphism group of D with X ≥G ≤Aut（X） where X ≌ PSL2（q）.Then D is a 2-（15,8,4） symmetric design with X = PSL2（9） and Xx = PGL2（3） where x is a point of D.
文摘In this paper,we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B,N and T,and we also compute the orders of them.Furthermore,we give explicit generators for the rational invariants fields of the Borel subgroup and the Neron-Severi subgroup of the general linear group.
文摘Let F q be a finite field with qelements where q=p~α. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (n+t,n)(F q), singular unitary group U (n+t,n)(F (q^2)) and singular orthogonal group O (n+t,n)(F q)(n is even) over finite fields F q.
文摘The main purpose of this paper is to extend to classical groups a H*irmander multiplier theorem concerning translation invariant operators on L p spaces which are known for the n-torus.
文摘The authors determine all the complete Langlands parameters corresponding to the representations of the classical groups with integral regular infintesimal characters, and get all L-packts in that case.
文摘Let G be a classical group over an arbitrary field F,acting on an n-dimensional vector space V=V(n,F)over a field F.In this paper,we classify the maximal subgroups of G,which normalizes a solvable subgroup N of GL(L,F)not lying in F^(*)1_(V).
基金funded by Scientific Research Project of Beijing Educational Committee(No.KM202110028004).
文摘Let G be a classical group over an arbitrary field F,acting on an n-dimensional F-space V=V(n,F).All those maximal subgroups of G are classified each of which normalizes a solvable subgroup N of GL(V/F)not lying in F^(*)1v.
基金国家杰出青年科学基金，the Research Fund for the Doctoral Program of Higher Education of China
文摘Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.
文摘This is the second part of a pedagogical introduction to the theory of buildings of Jacques Tits.We de ne a(B,N)pair and construct a building out of it.Then we give a description of Chevalley groups,their(B,N)pair and the associated buildings.We illustrates this theory with many examples from classical groups.
基金supported by Croatian Ministry of Science,Education and Sports(Grant No.#037-0372794-2804)
文摘This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturMly the classification of irreducible square integrable representations modulo cuspidal data obtained by Mceglin and the author of this article （2002）. The second aim of the paper is to give a description of an invariant （partially defined function） of irreducible square integrable representation of a classical p-adic group （defined by Mceglin using embeddings） in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group （which is related to deformation of Jordan blocks of representations）.
基金Supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute under Grant No. 408YKQ09the National Natural Science Foundation of China under Grant No. 10735030
文摘The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.
基金supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institutethe National Natural Science Foundation of China under Grant Nos. 10735030 and 90503006
文摘The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
基金the State Key Basic Research Program of China under Grant No.2004CB318000
文摘Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.
基金supported by National Natural Science Foundation of China under Grant Nos.10475055 and 90503006
文摘The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.
文摘Based on the symbolic computational system Maple, the similarity reductions of a Lax pair for the （2＋1 ）-dimensional differential Sawada Kotera （SK） equation by the classical Lie point group method, are presented. We obtain several interesting reductions. Comparing the reduced Lax pair＇s compatibility with the reduced SK equation under the same symmetry group, we find that the reduced Lax pairs do not always lead to the reduced SK equation. In general, the reduced equations are the subsets of the compatibility conditions of the reduced Lax pair.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475055 and 10547124 and partly by Shanghai Leading Academic Discipline Project under Grant No. T0401.Acknowledgments The authors would like to thank Prof. S.Y. Lou for his helpful discussions.
文摘We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.10875106
文摘In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equation to some （1 ＋ 1 ）-dimensional partial differential systems. Finally, many exact travelling solutions of the （2＋1）-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.
基金Supported by the National Natural Science Foundation of China under Grant No. 10735030Shanghai Leading Academic Discipline Project under Grant No. B412+2 种基金National Natural Science Foundation of China under Grant No. 90718041Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0734K.C. Wong Magna Fund in Ningbo University
文摘In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.
文摘Abstract homomorphisms between subgroups of algebraic groups were studied in detail by A.Borel, J.Tit.[1] and B.Wei.feile.[2] provided that the images of the homomorphisms are Zariski dense subsets and that the fields over which algebraic groups are defined are infinite. The purpose of this paper is to determine all embedding homomorphisms of SLn(k) into SLn(K) when k and K are any fields of the same characteristic, without assumption of Zariski density and infinitude of fields. The result in this paper generalizes a result of Chen Yu on homomorphisms of two dimensional linear groups[3].
基金This research was partially supported by the NNSF of China(No.11301061).
文摘Let F_(q)be a finite field of any characteristic and GL(n,F_(q))be the general linear group over F_(q).Suppose W denotes the standard representation of GL(n,F_(q)),and GL(n,F_(q))acts diagonally on the direct sum of W and its dual space W^(∗).Let G be any subgroup of GL(n,F_(q)).Suppose the invariant field F_(q)(W)G=F_(q)(f1,f2,…,fk),where f1,f2,…,fk in F_(q)[W]G are homogeneous invariant polynomials.We prove that there exist homogeneous polynomialsl1,l2,…,ln in the invariant ring F_(q)[W⊕W^(∗)]G such that the invariant field F_(q)(W⊕W^(∗))G is generated by{f1,f2,…,fk,l1,l2,…,ln}over F_(q).
