For a commutative ring with identity, we obtain a complete description of all overgroups of unitary groups U2nR (n ≥ 5), which include symplectic, ordinary orthogonal and standard unitary groups, in linear group GL2nR.
Let K, F be division rings, with KF,and dim_F K=r【∞ when we regard K asa left F-space. An n-dimensional left K-space V(n, K) can be regarded as annr-dimensional left space V= V(nr,F) over F,and thus GL (n, K) acting...Let K, F be division rings, with KF,and dim_F K=r【∞ when we regard K asa left F-space. An n-dimensional left K-space V(n, K) can be regarded as annr-dimensional left space V= V(nr,F) over F,and thus GL (n, K) acting on V(n, K)is embedded in GL (nr, F) acting on V (nr, F). In Ref. [1] we determined theovergroups of SL (n, K) and Sp (n, K) in GL(nr,F), Which are precisely the lineargroups or symplectic groups acting on the vector spaces structure V (nd, E)展开更多
定出了局部环上正交群中一类子群的扩群,得到了如下结果:设R是局部环,M是R的唯一极大理想,O(2m,R)为R上正交群.对R的任意理想S,G(2m,S)表示子群{A BC D∈O(2m,R)|B∈Sm×m}.如果char(R)≠2,m≥3,G(2m,0)≤X≤G(2m,M),那么存在R的理...定出了局部环上正交群中一类子群的扩群,得到了如下结果:设R是局部环,M是R的唯一极大理想,O(2m,R)为R上正交群.对R的任意理想S,G(2m,S)表示子群{A BC D∈O(2m,R)|B∈Sm×m}.如果char(R)≠2,m≥3,G(2m,0)≤X≤G(2m,M),那么存在R的理想S,使得X=G(2m,S).展开更多
This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces?G/H?with G = SL(n,R),H = GL(n-1,R)?. F...This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces?G/H?with G = SL(n,R),H = GL(n-1,R)?. For Hermitian symmetric spaces G/K, canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H, the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.展开更多
典型群理论是群论的重要组成部分,典型群的子群结构研究的目的是定出典型群的所有极大子群和扩群.讨论了主理想整环R上线性群GL(2m,R)的子群,得到如下结果:设R为主理想整环,m≥2,G(2m,S)=A BO D∈GL(2m,R)|A,D∈GL(m,R),B∈Sm×m,P(...典型群理论是群论的重要组成部分,典型群的子群结构研究的目的是定出典型群的所有极大子群和扩群.讨论了主理想整环R上线性群GL(2m,R)的子群,得到如下结果:设R为主理想整环,m≥2,G(2m,S)=A BO D∈GL(2m,R)|A,D∈GL(m,R),B∈Sm×m,P(2m,S)=G(2m,S)∩SL(2m,R),若P(2m,0)≤X≤G(2m,S),则存在R的理想T,U(R)的子群V,使得X=φ-T1(V).展开更多
基金supported by the National Natural Science Foundation(Grant No.10571033)the Research Fund for the Doctoral of Higher Education of China(Grant No.20040213006)Cultivation Fund of the Key Scientific and Technical Innovation Project Ministry of Education of China(Grant No.704004).
文摘For a commutative ring with identity, we obtain a complete description of all overgroups of unitary groups U2nR (n ≥ 5), which include symplectic, ordinary orthogonal and standard unitary groups, in linear group GL2nR.
文摘Let K, F be division rings, with KF,and dim_F K=r【∞ when we regard K asa left F-space. An n-dimensional left K-space V(n, K) can be regarded as annr-dimensional left space V= V(nr,F) over F,and thus GL (n, K) acting on V(n, K)is embedded in GL (nr, F) acting on V (nr, F). In Ref. [1] we determined theovergroups of SL (n, K) and Sp (n, K) in GL(nr,F), Which are precisely the lineargroups or symplectic groups acting on the vector spaces structure V (nd, E)
文摘定出了局部环上正交群中一类子群的扩群,得到了如下结果:设R是局部环,M是R的唯一极大理想,O(2m,R)为R上正交群.对R的任意理想S,G(2m,S)表示子群{A BC D∈O(2m,R)|B∈Sm×m}.如果char(R)≠2,m≥3,G(2m,0)≤X≤G(2m,M),那么存在R的理想S,使得X=G(2m,S).
文摘This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces?G/H?with G = SL(n,R),H = GL(n-1,R)?. For Hermitian symmetric spaces G/K, canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H, the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.
文摘典型群理论是群论的重要组成部分,典型群的子群结构研究的目的是定出典型群的所有极大子群和扩群.讨论了主理想整环R上线性群GL(2m,R)的子群,得到如下结果:设R为主理想整环,m≥2,G(2m,S)=A BO D∈GL(2m,R)|A,D∈GL(m,R),B∈Sm×m,P(2m,S)=G(2m,S)∩SL(2m,R),若P(2m,0)≤X≤G(2m,S),则存在R的理想T,U(R)的子群V,使得X=φ-T1(V).
