KMS Of Academy of mathematics and systems sciences, CAS
A Note on Integral Structures in Some Locally Algebraic Representations of GL(2) | |
Hu, Yong Quan1,2 | |
2020-03-24 | |
发表期刊 | ACTA MATHEMATICA SINICA-ENGLISH SERIES |
ISSN | 1439-8516 |
页码 | 14 |
摘要 | In the p-adic local Langlands correspondence for GL(2) (DOUBLE-STRUCK CAPITAL Q(p)), the following theorem of Berger and Breuil has played an important role: the locally algebraic representations of GL(2)(DOUBLE-STRUCK CAPITAL Q(p)) associated to crystabelline Galois representations admit a unique unitary completion. In this note, we give a new proof of the weaker statement that the locally algebraic representations admit at most one unitary completion and such a completion is automatically admissible. Our proof is purely representation theoretic, involving neither (phi, Gamma)-module techniques nor global methods. When F is a finite extension of DOUBLE-STRUCK CAPITAL Q(p), we also get a simpler proof of a theorem of Vigneras for the existence of integral structures for (locally algebraic) special series and for (smooth) tamely ramified principal series. |
关键词 | Invariant norm diagram |
DOI | 10.1007/s10114-020-8213-z |
收录类别 | SCI |
语种 | 英语 |
资助项目 | National Natural Science Foundation of China[11688101] ; China's Recruitement Program of Global Experts ; National Center for Mathematics and Interdisciplinary Sciences ; Hua Loo-Keng Center for Mathematical Sciences of Chinese Academy of Sciences |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics, Applied ; Mathematics |
WOS记录号 | WOS:000526189100001 |
出版者 | SPRINGER HEIDELBERG |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/51167 |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Hu, Yong Quan |
作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Hu, Yong Quan. A Note on Integral Structures in Some Locally Algebraic Representations of GL(2)[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2020:14. |
APA | Hu, Yong Quan.(2020).A Note on Integral Structures in Some Locally Algebraic Representations of GL(2).ACTA MATHEMATICA SINICA-ENGLISH SERIES,14. |
MLA | Hu, Yong Quan."A Note on Integral Structures in Some Locally Algebraic Representations of GL(2)".ACTA MATHEMATICA SINICA-ENGLISH SERIES (2020):14. |
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