split rank
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2019 ◽  
Vol 59 (2) ◽  
pp. 471-513
Author(s):  
Erik P. van den Ban ◽  
Job J. Kuit ◽  
Henrik Schlichtkrull

2019 ◽  
Vol 31 (2) ◽  
pp. 341-349
Author(s):  
Erik P. van den Ban ◽  
Job J. Kuit ◽  
Henrik Schlichtkrull

AbstractLet {G/H} be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for {G/H}. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of {G/H}.


2017 ◽  
Vol 21 (17) ◽  
pp. 467-533 ◽  
Author(s):  
Erik P. van den Ban ◽  
Job J. Kuit

2015 ◽  
Vol 154 (1-2) ◽  
pp. 273-303 ◽  
Author(s):  
Michele Conforti ◽  
Alberto Del Pia ◽  
Marco Di Summa ◽  
Yuri Faenza
Keyword(s):  

Author(s):  
Michele Conforti ◽  
Alberto Del Pia ◽  
Marco Di Summa ◽  
Yuri Faenza
Keyword(s):  

2012 ◽  
Vol 37 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Amitabh Basu ◽  
Gérard Cornuéjols ◽  
François Margot
Keyword(s):  

2011 ◽  
Vol 36 (3) ◽  
pp. 432-461 ◽  
Author(s):  
Santanu S. Dey ◽  
Quentin Louveaux
Keyword(s):  

2009 ◽  
Vol 61 (6) ◽  
pp. 1383-1406
Author(s):  
Eric Wambach

Abstract Gelbart and Piatetskii-Shapiro constructed various integral representations of Rankin–Selberg type for groups G×GLn, where G is of split rank n. Here we show that their method can equally well be applied to the product U3 × GL2, where U3 denotes the quasisplit unitary group in three variables. As an application, we describe which cuspidal automorphic representations of U3 occur in the Siegel induced residual spectrum of the quasisplit U4.


2009 ◽  
Vol 130 (1) ◽  
pp. 107-124 ◽  
Author(s):  
Santanu S. Dey
Keyword(s):  

2008 ◽  
Vol 60 (6) ◽  
pp. 1306-1335 ◽  
Author(s):  
Goran Muić

AbstractThis paper is the continuation of our previous work on the explicit determination of the structure of theta lifts for dual pairs (Sp2n,O(V)) over a non-archimedean field F of characteristic different than 2, where n is the split rank of Sp2n and the dimension of the space V (over F) is even. We determine the structure of theta lifts of tempered representations in terms of theta lifts of representations in discrete series.


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