Symplectic representations of algebraic groups satisfying a certain analyticity condition
Symplectic representations of algebraic groups satisfying a certain analyticity condition
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DOI：
10.1007/bf02395046
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发表时间：
1967-07
期刊：
影响因子：
3.7
通讯作者：
I. Satake
中科院分区：
文献类型：
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作者：
I. Satake
1. 本研究的起点是Kuga关于确定满足一定解析性条件的厄米特型半简单（代数）群的所有辛表示的问题（[8]；更精确的表述见6.1）。在我之前的论文[9]（[9 a]）中，我已经从几何的角度解决了这个问题，换句话说，在实数R(2)的域上解决了这个问题。但是，问题的目的是(i)部分由NSF资助GP 3903。(3) Mumford和Tate从一个稍微不同的角度考虑了一个类似的问题，并独立地得到了一个类似的分类（至少，对于满足条件（I-12）的绝对不可约表示），见Mumford，阿贝尔变种的族，纯数学研讨会论文集，1966年第9卷，347-351页。同时，在一些特殊情况下，一些数学家结合自同态函数的理论，研究了一个对称区域向另一个对称区域的全纯映射。Cf。[4],[7];还有艾勒的南希笔记。
1. The starting point of this study was a problem of Kuga on the determination of all symplectie representations of a semi-simple (algebraic) group of hermitian type satisfying a certain analytieity condition ([8]; for a more precise formulation, see 6.1). In my previous paper [9]([9 a]), I have solved this problem from the geometrical point of view, or in other words, over the field of real numbers R (2). But, the aim of the problem lying (i) Partly supported by NSF grant GP 3903.(3) Mumford and Tate have considered a similar problem from a somewhat different point of view and obtained a similar classification independently (at least, for absolutely irreducible representations satisfying the condition (I-12)), see Mumford, Families of abelian varieties, Proceedings of the Symposia in-Pure Mathematics, Vol. 9, 1966, 347-351. Meanwhile, in some special cases, holomorphie irabeddings of a symmetric domain into another symmetric domain have been studied by several mathematicians in connection with the theory of automorphie functions. Cf.[4],[7]; and also Eiehler's Nancy note.