scholarly journals Distinguished Representations of SO(n + 1,  1) × SO(n,  1), Periods and Branching Laws

2021 ◽  
pp. 291-320
Author(s):  
Toshiyuki Kobayashi ◽  
Birgit Speh
Keyword(s):  
Branching Laws ◽  
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 Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kei Yuen Chan
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Branching Laws ◽  
General Linear Groups ◽  
Branching Law

Abstract We prove a local Gan–Gross–Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier–Jacobi models and study a possible generalization to Ext-branching laws.

scholarly journals SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS

2018 ◽  
Vol 19 (5) ◽  
pp. 1521-1572
Author(s):  
Haruzo Hida ◽  
Jacques Tilouine
Keyword(s):  
Power Series ◽  
Galois Representation ◽  
Symmetric Power ◽  
Selmer Groups ◽  
Abelian Surfaces ◽  
Symmetric Powers ◽  
Branching Laws ◽  
Hida Family

We prove, under some assumptions, a Greenberg type equality relating the characteristic power series of the Selmer groups over $\mathbb{Q}$ of higher symmetric powers of the Galois representation associated to a Hida family and congruence ideals associated to (different) higher symmetric powers of that Hida family. We use $R=T$ theorems and a sort of induction based on branching laws for adjoint representations. This method also applies to other Langlands transfers, like the transfer from $\text{GSp}(4)$ to $U(4)$. In that case we obtain a corollary for abelian surfaces.

Branching Laws and Banking Offices: Comment

1979 ◽  
Vol 11 (2) ◽  
pp. 227 ◽  
Author(s):  
Donald T. Savage ◽  
David Burras Humphrey
Keyword(s):  
Branching Laws

scholarly journals Endoscopie et conjecture locale raffinée de Gan–Gross–Prasad pour les groupes unitaires

2015 ◽  
Vol 151 (7) ◽  
pp. 1309-1371 ◽  
Author(s):  
R. Beuzart-Plessis
Keyword(s):  
Unitary Groups ◽  
Branching Laws ◽  
Epsilon Factors

Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan–Gross–Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors.

scholarly journals Analysis on the minimal representation of O(p,q) II. Branching laws

2003 ◽  
Vol 180 (2) ◽  
pp. 513-550 ◽  
Author(s):  
Toshiyuki Kobayashi ◽  
Bent Ørsted
Keyword(s):  
Minimal Representation ◽  
Branching Laws
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