scholarly journals Strong multiplicity one theorems for locally homogeneous spaces of compact-type

2020 ◽  
Vol 148 (7) ◽  
pp. 3163-3173
Author(s):  
Emilio A. Lauret ◽  
Roberto J. Miatello
Keyword(s):  
Homogeneous Spaces ◽  
Compact Type ◽  
Multiplicity One ◽  
Strong Multiplicity ◽  
Locally Homogeneous

Strong multiplicity one for Siegel cusp forms of degree two

2021 ◽  
Vol 33 (5) ◽  
pp. 1157-1167
Author(s):  
Arvind Kumar ◽  
Jaban Meher ◽  
Karam Deo Shankhadhar
Keyword(s):  
Symplectic Group ◽  
Cusp Forms ◽  
Multiplicity One ◽  
Strong Multiplicity

Abstract We prove strong multiplicity one results for Siegel eigenforms of degree two for the symplectic group Sp 4 ⁡ ( ℤ ) {\operatorname{Sp}_{4}(\mathbb{Z})} .

scholarly journals Local real analysis in locally homogeneous spaces

2011 ◽  
Vol 138 (3-4) ◽  
pp. 477-528 ◽  
Author(s):  
Marco Bramanti ◽  
Maochun Zhu
Keyword(s):  
Homogeneous Spaces ◽  
Real Analysis ◽  
Locally Homogeneous

scholarly journals Unitary dual of GL(n) at archimedean places and global Jacquet–Langlands correspondence

2010 ◽  
Vol 146 (5) ◽  
pp. 1115-1164 ◽  
Author(s):  
A. I. Badulescu ◽  
D. Renard
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Multiplicity One ◽  
Unitary Dual ◽  
Strong Multiplicity ◽  
Local Results

AbstractIn a paper by Badulescu [Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations, Invent. Math. 172 (2008), 383–438], results on the global Jacquet–Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field were established, under the assumption that the local inner forms are split at archimedean places. In this paper, we extend the main local results of that article to archimedean places so that the above condition can be removed. Along the way, we collect several results about the unitary dual of general linear groups over ℝ, ℂ or ℍ which are of independent interest.

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