Character Relations for Distinguished Representations

1994 ◽  
Vol 116 (5) ◽  
pp. 1153 ◽  
Author(s):  
Jeffrey Hakim
Keyword(s):  
Distinguished Representations

scholarly journals Kirillov models for distinguished representations

1989 ◽  
Vol 116 ◽  
pp. 89-110 ◽  
Author(s):  
Courtney Moen
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Automorphic Forms ◽  
Principal Series ◽  
Weil Representation ◽  
Local Factors ◽  
Distinguished Representations ◽  
Group A ◽  
Local Representations ◽  
Covering Groups

In the theory of automorphic forms on covering groups of the general linear group, a central role is played by certain local representations which have unique Whittaker models. A representation with this property is called distinguished. In the case of the 2-sheeted cover of GL2, these representations arise as the the local components of generalizations of the classical θ-function. They have been studied thoroughly in [GPS]. The Weil representation provides these representations with a very nice realization, and the local factors attached to these representations can be computed using this realization. It has been shown [KP] that only in the case of a certain 3-sheeted cover do we find other principal series of covering groups of GL2 which have a unique Whittaker model. It is natural to ask if these distinguished representations also have a realization analgous to the Weil representation.

scholarly journals Gamma Factors, Root Numbers, and Distinction

2018 ◽  
Vol 70 (3) ◽  
pp. 683-701 ◽  
Author(s):  
Nadir Matringe ◽  
Omer Offen
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Quadratic Extension ◽  
Root Number ◽  
Converse Problem ◽  
Root Numbers ◽  
Special Values ◽  
Distinguished Representations ◽  
Local Invariants ◽  
Gamma Factor

AbstractWe study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of p-adic fields. We show that the local Rankin–Selberg root number of any pair of distinguished representation is trivial, and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at 1/2 is trivial for distinguished representations as well as the converse problem.

scholarly journals The characterization of theta-distinguished representations of GL(n)

2017 ◽  
Vol 222 (2) ◽  
pp. 551-598
Author(s):  
Eyal Kaplan
Keyword(s):  
Distinguished Representations

Distinguished representations for $\mathrm{SL}(n)$

2018 ◽  
Vol 25 (6) ◽  
pp. 1695-1717 ◽  
Author(s):  
U. K. Anandavardhanan ◽  
Dipendra Prasad
Keyword(s):  
Distinguished Representations

On the number of distinguished representations of a group element

1972 ◽  
Vol 39 (3) ◽  
pp. 521-527 ◽  
Author(s):  
David Jacobson ◽  
Kenneth S. Williams
Keyword(s):  
Group Element ◽  
Distinguished Representations

scholarly journals Distinguished representations for $SL(2)$

2003 ◽  
Vol 10 (6) ◽  
pp. 867-878 ◽  
Author(s):  
U. K. Anandavardhanan ◽  
Dipendra Prasad
Keyword(s):  
Distinguished Representations

Distinguished representations of metaplectic groups

1998 ◽  
Vol 120 (4) ◽  
pp. 723-755 ◽  
Author(s):  
Toshiaki Suzuki
Keyword(s):  
Metaplectic Groups ◽  
Distinguished Representations

scholarly journals Quaternion distinguished representations and unstable base change for unitary groups

2019 ◽  
Vol 202 ◽  
pp. 176-199
Author(s):  
Miyu Suzuki
Keyword(s):  
Base Change ◽  
Unitary Groups ◽  
Distinguished Representations

scholarly journals Distinguished representations and quadratic base change for $GL(3)$

1996 ◽  
Vol 348 (3) ◽  
pp. 913-939 ◽  
Author(s):  
Herve Jacquet ◽  
Yangbo Ye
Keyword(s):  
Base Change ◽  
Distinguished Representations

Distinguished representations of GL(n) and local converse theorems

2015 ◽  
Vol 148 (1-2) ◽  
pp. 1-27 ◽  
Author(s):  
Jeffrey Hakim ◽  
Omer Offen
Keyword(s):  
Converse Theorems ◽  
Distinguished Representations
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