2009-03-06

Luis Lomeli, University of Iowa

The Langlands-Shahidi method for the split classical groups over function fields

Abstract: The Langlands-Shahidi method over a global function field will be presented for the split classical groups. The case of a Siegel Levi subgroup of a classical group plays an important role in the theory. It gives a definition of the local L-functions and root numbers corresponding to the symmetric square and exterior square representations of the dual of GL(n,F), F a non-archimedean local field. When F has characteristic p, in joint work with G. Henniart, we prove that these factors agree with those arising on the Galois side by means of the local Langlands correspondence.