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

• Autores: David Soudry
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 1311-1326
• Idioma: inglés
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• Resumen

  • 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) GLn, 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 caseG = 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[m2 ].