scholarly journals On Some Degenerate Principal Series Representations of U(n,n)

1994 ◽  
Vol 126 (2) ◽  
pp. 305-366 ◽  
Author(s):  
S.T. Lee
Keyword(s):  
Principal Series ◽  
Series Representations ◽  
Degenerate Principal Series ◽  
Principal Series Representations

scholarly journals Analytic Continuation of Equivariant Distributions

2018 ◽  
Vol 2019 (23) ◽  
pp. 7160-7192 ◽  
Author(s):  
Dmitry Gourevitch ◽  
Siddhartha Sahi ◽  
Eitan Sayag
Keyword(s):  
Analytic Continuation ◽  
Reductive Group ◽  
Principal Series ◽  
Real Algebraic Varieties ◽  
Series Representations ◽  
Degenerate Principal Series ◽  
Special Case ◽  
Adic Case ◽  
Principal Series Representations ◽  
Whittaker Models

Abstract We establish a method for constructing equivariant distributions on smooth real algebraic varieties from equivariant distributions on Zariski open subsets. This is based on Bernstein’s theory of analytic continuation of holonomic distributions. We use this to construct H-equivariant functionals on principal series representations of G, where G is a real reductive group and H is an algebraic subgroup. We also deduce the existence of generalized Whittaker models for degenerate principal series representations. As a special case, this gives short proofs of existence of Whittaker models on principal series representations and of analytic continuation of standard intertwining operators. Finally, we extend our constructions to the p-adic case using a recent result of Hong and Sun.

EXPLICIT DOUBLING INTEGRALS FOR Sp2(F) AND $\widetilde{{{\rm Sp}}_{2}}(F)$ USING "GOOD TEST VECTORS"

2011 ◽  
Vol 07 (02) ◽  
pp. 449-527 ◽  
Author(s):  
CHRISTIAN ZORN
Keyword(s):  
Finite Extension ◽  
Principal Series ◽  
Good Test ◽  
Dual Pairs ◽  
Series Representations ◽  
Degenerate Principal Series ◽  
Doubling Method ◽  
Test Vectors ◽  
Metaplectic Cover ◽  
Principal Series Representations

In this paper, we offer some explicit computations of a formulation of the doubling method of Piatetski-Shapiro and Rallis for the groups Sp 2(F) (the rank 2 symplectic group) and its metaplectic cover [Formula: see text] for F a finite extension of ℚp with p ≠ 2. We determine a set of "good test vectors" for the irreducible constituents of unramified principal series representations for these groups as well as a set of "good theta test sections" in a family of degenerate principal series representations of Sp 4(F) and [Formula: see text]. Determining "good test data" that produces a non-vanishing doubling integral should indicate the existence of a non-vanishing theta lifts for dual pairs of the type ( Sp 2(F), O (V)) (respectively [Formula: see text]) where V is a quadratic space of an even (respectively odd) dimension.

Sign in / Sign up

Export Citation Format

Share Document