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
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.
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
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)
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.
