Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators

Xiaoxiang Yu

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Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators

机译：拟分裂古典群和交织算子的极点的预齐性

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Suppose that P= MN is a maximal parabolic subgroup of a quasisplit, connected, reductive classical group G defined over a non-Archimedean field and A is the standard intertwining operator attached to a tempered representation of G induced from M. In this paper we determine all the cases in which Lie(N) is prehomogeneous under Ad(m) when N is non-abelian, and give necessary and sufficient conditions for A to have a pole at 0.

机译：假设P = MN是在非阿基米德场上定义的拟分裂，连通的，还原性经典群G的最大抛物子群，并且A是附着于由M诱发的G的修正表示形式的标准交织算子。当N是非阿贝尔的时，所有在Lie（N）在Ad（m）下都是同质的情况，并给出A的极点为0的充要条件。

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《Canadian Journal of Mathematics》 |2009年第3期|共17页
作者
Xiaoxiang Yu;
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正文语种 eng
中图分类数学;
关键词
Prehomogeneity; Groups; Intertwining Operators;

机译：前同质;群;交织算子;

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专利

1. Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators [J] . Xiaoxiang Yu Canadian Journal of Mathematics . 2009,第3期

机译：拟分裂古典群和交织算子的极点的预齐性
2. Poles of intertwining operators via endoscopy; the connection with prehomogeneous vector spaces with an appendix, 'Basic endoscopic data', by Diana Shelstad - To the memory of Magdy Assem [J] . Shahidi F. Compositio mathematica . 2000,第3期

机译：通过内窥镜检查交织在一起的操作员戴安娜·谢尔斯塔德（Diana Shelstad）通过附录“基本内窥镜数据”与前同质向量空间的联系-献给Magdy Assem
3. Residues of standard intertwining operators on p-adic classical groups [J] . Yu Xiaoxiang Forum mathematicum . 2016,第4期

机译：p-adic古典群上标准交织算子的残差
4. Induced Representations, Intertwining Operators and Transfer [C] . James Arthur Conference on Group Representations, Ergodic Theory, and Mathematical Physics . 2008

机译：诱发的表示，交织运营商和转移
5. Intertwining vertex operators and representations of affine Lie algebras. [D] . Calinescu, Nicoleta Corina. 2006

机译：纠缠的顶点算子和仿射李代数的表示。
6. Indefinite intertwining operators [O] . M. W. Baldoni-Silva, A. W. Knapp 1984

机译：不确定的缠绕算子
7. with an Appendix “L-Functions and Poles of Intertwining Operators” [O] . Steven Spallone, Freydoon Shahidi 2015

机译：附录“L-函数和交织操作符的极点”

Prehomogeneity on Quasi-Split Classical Groups and Poles of Intertwining Operators

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