Mathematics

Prof. Luis Lomeli
Pontificia Universidad Catolica De Valparaiso

Globalizations methods are of utmost importance in the Langlands Program, for example, these are used in the proof of the local Langlands correspondence for GL(n). In one direction, we are now able to globalize any supercuspidal representation of a connected reductive group in characteristic p, by the work of Henniart-Lomeli and Gan-Lomeli. And, in another direction, we take a look at an example where, using a technique of Henniart-Lomeli, we can use globalization methods in characteristic zero, as well as characteristic p, and prove compatibility of Langlands-Shahidi local L-functions with those arising from the Galois side of the local Langlands correspondence.