English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Small automorphic representations and degenerate Whittaker vectors

Gustafsson, H. P. A., Kleinschmidt, A., & Persson, D. (2016). Small automorphic representations and degenerate Whittaker vectors. Journal of Number Theory, 166, 344-399. doi:10.1016/j.jnt.2016.02.002.

Item is

Files

show Files
hide Files
:
1412.5625.pdf (Preprint), 2MB
Name:
1412.5625.pdf
Description:
File downloaded from arXiv at 2015-01-06 12:17
OA-Status:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
:
JNT166_344.pdf (Publisher version), 728KB
 
File Permalink:
-
Name:
JNT166_344.pdf
Description:
-
OA-Status:
Visibility:
Restricted (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), MPGR; )
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show

Creators

show
hide
 Creators:
Gustafsson, Henrik P. A., Author
Kleinschmidt, Axel1, Author           
Persson, Daniel, Author
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

Content

show
hide
Free keywords: Mathematics, Number Theory, math.NT,High Energy Physics - Theory, hep-th,Mathematics, Representation Theory, math.RT
 Abstract: We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain degenerate Whittaker vectors on G. Although we expect our results to hold for arbitrary simply-laced groups, we give complete proofs only for G=SL(3) and G=SL(4). This is based on a method of Ginzburg that associates Fourier coefficients of automorphic forms with nilpotent orbits of G. Our results complement and extend recent results of Miller and Sahi. We also use our formalism to calculate various local (real and p-adic) spherical vectors of minimal representations of the exceptional groups E_6, E_7, E_8 using global (adelic) degenerate Whittaker vectors, correctly reproducing existing results for such spherical vectors obtained by very different methods.

Details

show
hide
Language(s):
 Dates: 2014-12-1720152016
 Publication Status: Issued
 Pages: 55 pages
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Journal of Number Theory
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 166 Sequence Number: - Start / End Page: 344 - 399 Identifier: -