Abstract
There are described the subgroups of the general symplectic group Γ=GSp(2n, R) over a commutative semilocal ring R, containing the group of symplectic diagonal matrices. For each such subgroup P there is uniquely defined a symplectic D-net a such that Γ(σ)⩽p⩽NΓ(σ), where Γ (σ) is the net subgroup in Γ corresponding to σ (cf. RZhMat, 1977, 5A288), and NΓ(σ) is its normalizer. The quotient group NΓ × (σ)/Γ(σ) is calculated. There are also considered subgroups in Sp(2n, R). Analogous results for subgroups of the general linear group were obtained earlier in RZhMat, 1978, 9A237.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 31–47, 1980.
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Vavilov, N.A., Dybkova, E.V. Subgroups of the general symplectic group containing the group of diagonal matrices. J Math Sci 24, 406–416 (1984). https://doi.org/10.1007/BF01094368
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DOI: https://doi.org/10.1007/BF01094368