Rankin-Selberg integrals, the descent method, and Langlands functoriality

Research output: Contribution to conferencePaperpeer-review

Abstract

In this article I survey the descent method of Ginzburg, Rallis and Soudry and its main applications to the Langlands functorial lift of automorphic, cuspidal, generic representations on a classical group to (appropriate) GL n, and to establishing a local Langlands reciprocity law for (split) SO2n+1 (joint work with D. Jiang). The descent method arises when we consider certain residues of special cases of a family of global integrals, attached to pairs of automorphic, cuspidal representations, one on a classical group G and one on GLn. The last part of this article focuses on the case G = SOm (split), and the progress made in a joint work with S. Rallis, towards establishing, via the converse theorem, the functorial lift from any automorphic, cuspidal representation on G to GL2[m/2].

Original languageEnglish
Pages1311-1325
Number of pages15
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: 22 Aug 200630 Aug 2006

Conference

Conference25th International Congress of Mathematicians, ICM 2006
Country/TerritorySpain
CityMadrid
Period22/08/0630/08/06

Keywords

  • Descent method
  • Functorial lift
  • Gelfand-Graev models
  • L-functions

Fingerprint

Dive into the research topics of 'Rankin-Selberg integrals, the descent method, and Langlands functoriality'. Together they form a unique fingerprint.

Cite this