scholarly journals Splittings of the metaplectic covers of some reductive dual pairs

2001 ◽  
Vol 199 (1) ◽  
pp. 163-226 ◽  
Author(s):  
Shu-Yen Pan
Keyword(s):  
Dual Pairs ◽  
Reductive 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.

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.

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