scholarly journals The explicit theta correspondence for reductive dual pairs (Sp(p,q),O⁎(4))

2016 ◽  
Vol 271 (9) ◽  
pp. 2422-2459 ◽  
Author(s):  
Yixin Bao
Keyword(s):  
Theta Correspondence ◽  
Dual Pairs ◽  
Reductive Dual Pairs

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.

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.

scholarly journals Finite-reductive dual pairs in G2

2002 ◽  
Vol 340 (1-3) ◽  
pp. 123-136
Author(s):  
L. Barchini ◽  
Mark R. Sepanski
Keyword(s):  
Dual Pairs ◽  
Reductive Dual Pairs

scholarly journals Correspondences of the Gelfand invariants in reductive dual pairs

2003 ◽  
Vol 75 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Minoru Itoh
Keyword(s):  
Dual Pair ◽  
Explicit Description ◽  
Universal Enveloping Algebras ◽  
Dual Pairs ◽  
Enveloping Algebras ◽  
Central Elements ◽  
Reductive Dual Pairs

AbstractFor each complex reductive dual pair introduced by R. Howe, this paper presents a formula for the central elements of the universal enveloping algebras given by I. M. Gelfand. This formula provides an explicit description of the correspondence between the ‘centers’ of the two universal enveloping algebras.

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.

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