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 language | English |
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Pages | 1311-1325 |
Number of pages | 15 |
State | Published - 2006 |
Event | 25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: 22 Aug 2006 → 30 Aug 2006 |
Conference
Conference | 25th International Congress of Mathematicians, ICM 2006 |
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Country/Territory | Spain |
City | Madrid |
Period | 22/08/06 → 30/08/06 |
Keywords
- Descent method
- Functorial lift
- Gelfand-Graev models
- L-functions