scholarly journals A note on the local theta correspondence for unitary similitude dual pairs

2013 ◽  
Vol 133 (9) ◽  
pp. 3057-3064
Author(s):  
Chong Zhang
Keyword(s):  
Theta Correspondence ◽  
Dual Pairs

Supercuspidal representations and preservation principle of theta correspondence

2019 ◽  
Vol 2019 (750) ◽  
pp. 1-52
Author(s):  
Shu-Yen Pan
Keyword(s):  
Unitary Group ◽  
Orthogonal Group ◽  
Classical Groups ◽  
Theta Correspondence ◽  
Dual Pairs ◽  
Supercuspidal Representations ◽  
Explicit Characterization ◽  
A Chain

Abstract The preservation principle of the local theta correspondence predicts the existence of a chain of irreducible supercuspidal representations of p-adic classical groups. In this paper, we give an explicit characterization of the chain starting from an irreducible supercuspidal representations of a unitary group of one variable or an orthogonal group of two variables. In particular, we define the Lusztig-like correspondence of generic cuspidal data for p-adic groups and establish its relation with local theta correspondence of supercuspidal representations for p-adic dual pairs.

Theta correspondence for p-adic dual pairs of type I

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Petar Bakić ◽  
Marcela Hanzer
Keyword(s):  
Local Field ◽  
Type I ◽  
Admissible Representation ◽  
Theta Correspondence ◽  
Dual Pairs ◽  
Langlands Parameters ◽  
First Occurrence ◽  
Unitary Dual ◽  
Howe Correspondence ◽  
Irreducible Admissible Representation

Abstract We describe explicitly the Howe correspondence for the symplectic-orthogonal and unitary dual pairs over a nonarchimedean local field of characteristic zero. More specifically, for every irreducible admissible representation of these groups, we find its first occurrence index in the theta correspondence and we describe, in terms of their Langlands parameters, the small theta lifts on all levels.

First Occurrence for the Dual Pairs (U(p, q), U(r, s))

1999 ◽  
Vol 51 (3) ◽  
pp. 636-657 ◽  
Author(s):  
Annegret Paul
Keyword(s):  
Theta Correspondence ◽  
Dual Pairs ◽  
First Occurrence

AbstractWe prove a conjecture of Kudla and Rallis about the first occurrence in the theta correspondence, for dual pairs of the form (U(p, q), U(r, s)) and most representations.

L-Functoriality for Local Theta Correspondence of Supercuspidal Representations with Unipotent Reduction

2017 ◽  
Vol 69 (1) ◽  
pp. 186-219
Author(s):  
Shu-Yen Pan
Keyword(s):  
Classical Groups ◽  
Theta Correspondence ◽  
Dual Pairs ◽  
Supercuspidal Representations ◽  
Langlands Parameters ◽  
Reductive Dual Pairs ◽  
Theta Correspondences

AbstractThe preservation principle of local theta correspondences of reductive dual pairs over a p-adic field predicts the existence of a sequence of irreducible supercuspidal representations of classical groups. Adams and Harris-Kudla-Sweet have a conjecture about the Langlands parameters for the sequence of supercuspidal representations. In this paper we prove modified versions of their conjectures for the case of supercuspidal representations with unipotent reduction.

Explicit Solvability of Dual Pairs of Infinite Linear Programs

OPSEARCH ◽  
2005 ◽  
Vol 42 (3) ◽  
pp. 288-296
Author(s):  
K. C. Sivakumar ◽  
J. Mercy Swarna
Keyword(s):  
Linear Programs ◽  
Dual Pairs ◽  
Infinite Linear
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