**Title:** Nonlinear Fourier-Deligne transforms

**Speaker:** Shuyang Cheng

**Speaker Info:** University of Chicago

**Brief Description:** Nonlinear Fourier-Deligne transforms

**Special Note**:

**Abstract:**

In the approach of Godement-Jacquet to the study of principal L-functions on GL(n), the classical Fourier transform on the vector space M(n) of n-by-n matrices has played a special role, which leads in particular to the local and global functional equations of such L-functions.More generally for automorphic L-functions on GL(n) associated with a representation r of the dual group, there exists a monoid M(r) containing GL(n) which plays the role of M(n), and one expects there to exist nonlinear analogues of Fourier transforms on M(r).

Such nonlinear Fourier transforms, together with analogues over finite fields, namely nonlinear Fourier-Deligne transforms, have been constructed by Braverman-Kazhdan. In this talk I will recall the theory of such nonlinear Fourier-Deligne transforms and give a proof for a conjecture of Braverman-Kazhdan which essentially says that nonlinear Fourier-Deligne transforms commute with parabolic induction. This is joint work with B.C. Ngo.

Copyright © 1997-2024 Department of Mathematics, Northwestern University.