Title: Local (L-, \epsilon- and \gamma-) factors, and converse theorems.
Abstract: Our first goal will be to define local (L-,\epsilon- and \gamma-) factors and to study their properties. These factors are needed to formulate the local Langlands correspondence for GL(n), which was outlined two weeks ago. We will do it first for supercuspidal representations of GL(n) and then for local Galois representations, that is, for representations of Gal(\bar{F}/F), where F is a local field.
Then we will state global converse theorems, generalizing the classical Weil and Hecke converse theorems, appearing in the previous lecture.
If time permits, we will discuss some applications of converse theorems and some open
converse problems.
The talk will be mostly independent of the previous one.
Key words: Generic representations, Whittaker model, L- and \epsilon-factors,
local gamma factor, Local and global converse theorems