A Note on Integral Structures in Some Locally Algebraic Representations of GL(2)

doi:10.1007/s10114-020-8213-z

CSpace

	A Note on Integral Structures in Some Locally Algebraic Representations of GL(2)
	Hu, Yong Quan 1,2
	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.