Global Theta Liftings of General Linear Groups
Global Theta Liftings of General Linear Groups
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一般线性群的全局 Theta 提升
DOI：
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发表时间：
1996
影响因子：
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通讯作者：
Takao Watanabe
中科院分区：
文献类型：
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作者：
Takao Watanabe
研究了一类不可约2型对偶约化对的整体θ提升问题。证明了给定的不可约自守尖形表示的整体θ提升的象是非零的当且仅当它的标准L-函数在点1/2处非零，并且该象与初始自守尖形表示重合.作为这一结果的推论，得到了全局Howe相关.
A global theta lifting of some irreducible type 2 dual reductive pair is studied. It is proved that the image of a global theta lifting of a given irreducible automorphic cuspidal representation is non- vanishing if and only if its standard L-function is nonzero at the point 1/2,and then the image coincides with the initial automorphic cuspidal representation. As a corollary of this result,the global Howe correspon- dence is obtained.