# Felix Klein Lectures

## On Langlands Functoriality from classical groups to GL(n)

### David Soudry, School of Mathematical Siences Tel Aviv University

**Date: **May 18 - June 17, Wednesday and Friday, 10:00 - 12:00

**Venue: **Seminarraum A, Beringstraße 4

### Abstract:

The principle of Langlands functoriality predicts the existence of a (functorial) lift of automorphic representations on a classical group G to automorphic representations on GL(n) for an appropriate n and characterizes the image of such a lifting map. There are two approaches to this fundamental problem. The first is through the Arthur-Selberg trace formula. The second is through the theory of L-functions. In these lectures we will focus on the second approach.

We will survey the work of Cogdell, Kim, Piatetski-Shapiro and Shahidi, which proves the existence of a weak lift from cuspidal generic automorphic representations of split classical groups to GL(n). Then we will introduce the descent method of Ginzburg, Rallis and Soudry, which provides an explicit map in the reverse direction, and, in particular, we will find the image of the above weak lift. The descent construction is tied to certain global integrals, of Rankin-Selberg type, or of Shimura type, which represent L-functions of pairs of cuspidal representations, one on G and the other on GL(n). We will also survey these integrals, as well as their p-adic counterparts.