LOCAL THETA CORRESPONDENCES BETWEEN SUPERCUSPIDAL REPRESENTATIONS

Loke Hung Yean; Ma Jia-Jun

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LOCAL THETA CORRESPONDENCES BETWEEN SUPERCUSPIDAL REPRESENTATIONS

机译：Supercuspidal表示之间的本地θ

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By the works of Yu, Kim and Hakim-Murnaghan, we have a parameterization and construction of all supercuspidal reprsentations of a reductive p-adic group in terms of supercuspidal data, when p is sufficiently large. In this paper, we will define a correspondence of supercuspidal data via moment maps and theta correspondences over finite fields. Then we will show that local theta correspondences between supercuspidal representations are completely described by this notion. In Appendix B, we give a short proof of a result of Pan on "depth preservation".

机译：由Yu，Kim和Hakim-Murnaghan的作品，当P足够大时，我们有一个参数化和构建还原性P-ADIC组的所有超高次数鉴定。在本文中，我们将通过在有限字段上通过时刻映射和Theta对应方式定义SuperCuspidal数据的对应关系。然后，我们将表明，这一概念完全描述了SuperCuspidal表示之间的本地θ对应关系。在附录B中，我们在“深度保存”上给出了PAN的结果。

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《Annales scientifiques de l'Ecole normale superieure》 |2018年第4期|共65页
作者
Loke Hung Yean; Ma Jia-Jun;
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作者单位

Natl Univ Singapore Dept Math 2 Sci Dr 2 Singapore 117543 Singapore;

Shanghai Jiao Tong Univ Sch Math Sci 800 Dongchuan RD Shanghai 200240 Peoples R China;

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正文语种 eng
中图分类自然科学总论;师范教育理论;
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1. LOCAL THETA CORRESPONDENCES BETWEEN SUPERCUSPIDAL REPRESENTATIONS [J] . Loke Hung Yean, Ma Jia-Jun Annales scientifiques de l'Ecole normale superieure . 2018,第4期

机译：Supercuspidal表示之间的本地θ
2. Supercuspidal representations and preservation principle of theta correspondence [J] . Shu-YenPan Journal fur die Reine und Angewandte Mathematik . 2019,第750期

机译：Supercuspidal表示和θ对应的保存原理
3. Base change and theta-correspondences for supercuspidal representations of SL(2) [J] . Manderscheid D. Journal of Algebra . 2013,第Null期

机译：SL（2）的超尖峰表示的基础变化和theta对应
4. On the support of matrix coefficients of supercuspidal representations of the general linear group over a local non-archimedean field [C] . Erez Lapid Conference on Representation Theory and Algebraic Geometry . 2019

机译：在局部非Archimedean场上的一般线性群体超鲜谱表示矩阵系数的支持
5. A notion of rank for enveloping algebras and local theta correspondence. [D] . Protsak, Victor A. 2000

机译：包围代数和局部theta对应关系的等级概念。
6. Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between complex spike cells and theta cells [O] . Luísa Castro, Paulo Aguiar 2011

机译：通过加速局部θ节律进行相位进动：复杂棘突细胞与θ细胞之间相互作用的生物物理模型
7. Local theta correspondences between epipelagic supercuspidal representations [O] . Loke, Hung Yean, Ma, Jia-jun, Savin, Gordan 2015

机译：epipelagic supercuspidal之间的局部theta对应交涉

LOCAL THETA CORRESPONDENCES BETWEEN SUPERCUSPIDAL REPRESENTATIONS

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