Meromorphic Basis of H-Invariant Distribution Vectors for the Generalized Principal Series of Reductive Symmetrical Spaces: Functional Equation
Meromorphic Basis of H-Invariant Distribution Vectors for the Generalized Principal Series of Reductive Symmetrical Spaces: Functional Equation
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约简对称空间广义主级数H不变分布向量的亚纯基：泛函方程
DOI：
10.1006/jfan.1994.1065
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发表时间：
1994
影响因子：
1.7
通讯作者：
P. Delorme
中科院分区：
文献类型：
--
作者：
Jacques Carmona;P. Delorme
设G是定义在R上的约化代数群的真实的点群，σ是G的对合，θ是G的Cartan对合，与σ可交换。设H是σ的不动点群的开子群。对G的一个σθ-稳定抛物子群P的诱导表示的H-不动分布向量空间建立了一个亚纯基。为此，我们采用一种方法，将Bruhat论文的应用范围（特别是推广到广义主级数的不可约性问题）加以扩展.亚纯性是通过我们建立的一个函数方程得到的，它推广了E.货车den Ban在P是极小σθ-稳定的情形下的一个推广.
Abstract Let G be the group of real points of a reductive algebraic group defined over R , σ an involution of G, and θ a Cartan involution of G commuting with σ. Let H be an open subgroup of the group of fixed points for σ. One builds a meromorphic basis for the space of H-fixed distributions vectors of induced representations from a σθ-stable parabolic subgroup P of G. For this, we use a method which extends the domain of application of Bruhat′s thesis (in particular, to the irreducibility problem for generalized principal series). The meromorphy is obtained by means of a functional equation that we establish and which generalizes the equation obtained by E. van den Ban in the case when P is minimal σθ-stable.