The Descent Map from Automorphic Representations of GL(n) to Classical Groups

10.1142/7742 ◽  
2011 ◽  
Author(s):  
David Ginzburg ◽  
Stephen Rallis ◽  
David Soudry
Keyword(s):  
Classical Groups ◽  
Automorphic Representations

scholarly journals On the global Gan-Gross-Prasad conjecture for general spin groups

2018 ◽  
Author(s):  
◽  
Melissa Emory
Keyword(s):  
Classical Groups ◽  
Spin Groups ◽  
Automorphic Representations ◽  
Spin Group ◽  
Central Value ◽  
Period Integral

In the 1990s, Benedict Gross and Dipendra Prasad formulated an intriguing conjecture connected with restriction laws for automorphic representations of a particular group. More recently, Gan, Gross, and Prasad extended this conjecture, now known as the Gan-Gross-Prasad Conjecture, to the remaining classical groups. Roughly speaking, they conjectured the non-vanishing of a certain period integral is equivalent to the non-vanishing of the central value of a certain L- function. Ichino and Ikeda refined the conjecture to give an explicit relationship between this central value of a L-function and the period integral. We propose a similar conjecture for a nonclassical group, the general spin group, and prove one case.

scholarly journals A reciprocal branching problem for automorphic representations and global Vogan packets

2020 ◽  
Vol 2020 (765) ◽  
pp. 249-277 ◽  
Author(s):  
Dihua Jiang ◽  
Baiying Liu ◽  
Bin Xu
Keyword(s):  
Irreducible Representation ◽  
Symmetry Breaking ◽  
Descent Method ◽  
Classical Groups ◽  
Orthogonal Groups ◽  
Automorphic Representations ◽  
Branching Rule ◽  
Branching Problem

AbstractLet G be a group and let H be a subgroup of G. The classical branching rule (or symmetry breaking) asks: For an irreducible representation π of G, determine the occurrence of an irreducible representation σ of H in the restriction of π to H. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation σ of H, find an irreducible representation π of G such that σ occurs in the restriction of π to H. For automorphic representations of classical groups, the branching problem has been addressed by the well-known global Gan–Gross–Prasad conjecture. In this paper, we investigate the reciprocal branching problem for automorphic representations of special orthogonal groups using the twisted automorphic descent method as developed in [13]. The method may be applied to other classical groups as well.

scholarly journals On fields of rationality for automorphic representations

2014 ◽  
Vol 150 (12) ◽  
pp. 2003-2053 ◽  
Author(s):  
Sug Woo Shin ◽  
Nicolas Templier
Keyword(s):  
Isomorphism Class ◽  
Discrete Series ◽  
Automorphic Representation ◽  
Linear Groups ◽  
Classical Groups ◽  
Automorphic Representations ◽  
General Linear Groups ◽  
Mild Conditions ◽  
Finite Set ◽  
Level Aspect

AbstractThis paper proves two results on the field of rationality$\mathbb{Q}({\it\pi})$for an automorphic representation${\it\pi}$, which is the subfield of$\mathbb{C}$fixed under the subgroup of$\text{Aut}(\mathbb{C})$stabilizing the isomorphism class of the finite part of${\it\pi}$. For general linear groups and classical groups, our first main result is the finiteness of the set of discrete automorphic representations${\it\pi}$such that${\it\pi}$is unramified away from a fixed finite set of places,${\it\pi}_{\infty }$has a fixed infinitesimal character, and$[\mathbb{Q}({\it\pi}):\mathbb{Q}]$is bounded. The second main result is that for classical groups,$[\mathbb{Q}({\it\pi}):\mathbb{Q}]$grows to infinity in a family of automorphic representations in level aspect whose infinite components are discrete series in a fixed$L$-packet under mild conditions.

Classical Groups, Derangements and Primes

2015 ◽  
Author(s):  
Timothy C. Burness ◽  
Michael Giudici
Keyword(s):  
Classical Groups

scholarly journals TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS

2021 ◽  
Author(s):  
R. H. EGGERMONT ◽  
A. SNOWDEN
Keyword(s):  
Classical Groups ◽  
Infinite Rank ◽  
Polynomial Representations ◽  
Algebraic Representations

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.

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