Completeness of Poincaré Series for Automorphic Forms Associated to the Integrable Discrete Series
Completeness of Poincaré Series for Automorphic Forms Associated to the Integrable Discrete Series
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与可积离散级数相关的自同构庞加莱级数的完备性
DOI：
10.1007/978-1-4684-6730-7_16
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
J. Wolf
中科院分区：
文献类型：
--
作者：
N. Wallach;J. Wolf
两年前,狼[11]研究了庞加莱系列运营商ϑ均匀全纯向量bundleE➛D /旗域D = G / V和任意离散群Г⊂G .他指出人生➛D非退化(见下文),如果G作用于平方可积空间上同调硫化氢(D, E)的可积离散系列表示,在年代最大的复杂尺寸紧凑亚变种K / V D,然后每Г自同构的Lpcohomology类ψ∈Hps(Г\ D;E), 1≤p≤∞，由poincar<s:1>级数表示
A couple of years ago, Wolf [11] studied the Poincaré series operator ϑ for a homogeneous holomorphic vector bundleE➛ D over a flag domain D = G/V and an arbitrary discrete subgroup Г⊂ G. He showed that ifE➛ D is nondegenerate (see below), and if G acts on the square integrable cohomology space H2s(D;E) by an integrable discrete series representation, where s is the complex dimension of the maximal compact subvariety K/V in D, then every Г-automorphic Lpcohomology class ψ∈ Hps(Г\D;E), 1 ⩽ p ⩽ ∞, is represented by a Poincaré series