KTGU数学特別講義(保型表現論)Globalization of supercuspidal representations over function fields and applications

2015/12/08 Tue 15:00 - 17:00
2015/12/15 Tue 15:00 - 17:00
2015/12/18 Fri 15:00 - 17:00
2015/12/22 Tue 15:00 - 17:00
2016/01/05 Tue 15:00 - 17:00
Wee Teck Gan
National University of Singapore

I will describe how one can use Poincare series to construct cuspidal automorphic representations of connected reductive group over a global function field with a given supercuspidal local component and prescribed behavior (such as ramification) at all other places. This globalization result can be used to complete the Langlands-Shahidi theory over function fields (a recent result of Luis Lomeli). Combining this with the recent construction by Vincent Lafforgue of the global Langlands correspondence over function fields, one can prove stability of arbitrary Langland-Shahidi gamma factors and obtain the local Langlands correspondence for classical groups. I will discuss some of these applications and if time permits (for me to understand it), I will give a sketch of the Lafforgue's construction.