A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups...A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.展开更多
Structures of two classes of solvable subgroups in SL（3, C） are given in this paper, and the integrability of the 3-order Fuchsian equation which is integrable in the sense that its monodromy group is solvable is di...Structures of two classes of solvable subgroups in SL（3, C） are given in this paper, and the integrability of the 3-order Fuchsian equation which is integrable in the sense that its monodromy group is solvable is discussed.展开更多
In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζ...In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.展开更多
We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields.We prove that the orbits of these solutions under the natural conjugation action of the gener...We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields.We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can be separated by classical conjugation invariants defined by characteristic polynomials.We also find a generating set for the vanishing ideal of these orbits.展开更多
In this paper,we present a very simple explicit description of Langlands Eisenstein series for SL(n,Z).The functional equations of these Eisenstein series are heuristically derived from the functional equations of cer...In this paper,we present a very simple explicit description of Langlands Eisenstein series for SL(n,Z).The functional equations of these Eisenstein series are heuristically derived from the functional equations of certain divisor sums and certain Whittaker functions that appear in the Fourier coefficients of the Eisenstein series.We conjecture that the functional equations are unique up to a real affine transformation of the s variables defining the Eisenstein series and prove the uniqueness conjecture in certain cases.展开更多
Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×...Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×n in FRn, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of U^×n in FR^n.展开更多
文摘A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.
文摘Structures of two classes of solvable subgroups in SL（3, C） are given in this paper, and the integrability of the 3-order Fuchsian equation which is integrable in the sense that its monodromy group is solvable is discussed.
基金Supported by the Tianyuan Fund for Mathematics of NSFC(11126273)Supported by the NSF of Henan Educational Committee(2011B110011)Supported by the Doctor Foundation of Henan University of Technology(2009BS029)
文摘In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then (i) InnG ■ K ■ AutG;(ii) AutG/K≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.
基金supported by the NNSF of China(Grant No.11401087).
文摘We exhibit an explicit formula for the cardinality of solutions to a class of quadratic matrix equations over finite fields.We prove that the orbits of these solutions under the natural conjugation action of the general linear groups can be separated by classical conjugation invariants defined by characteristic polynomials.We also find a generating set for the vanishing ideal of these orbits.
基金supported by Simons Collaboration(Grant No.567168)。
文摘In this paper,we present a very simple explicit description of Langlands Eisenstein series for SL(n,Z).The functional equations of these Eisenstein series are heuristically derived from the functional equations of certain divisor sums and certain Whittaker functions that appear in the Fourier coefficients of the Eisenstein series.We conjecture that the functional equations are unique up to a real affine transformation of the s variables defining the Eisenstein series and prove the uniqueness conjecture in certain cases.
基金Supported by National Natural Science Foundation of China(Grant No.11301195)a research foundation of Huaqiao University(Grant No.2014KJTD14)
文摘Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ＋ V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^×n in FRn, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of U^×n in FR^n.
