Orateur
Description
In the representation theory of finite reductive groups, an essential role is played by Lusztig's nonabelian Fourier transform, an involution on the space of unipotent characters of the group. For reductive p-adic groups, the unipotent local Langlands correspondence gives a natural parametrization of irreducible smooth representations with unipotent cuspidal support. However, many questions about the characters of these representations are still open. In joint work with Anne-Marie Aubert and Dan Ciubotaru, we propose a potential lift of Lusztig's Fourier transform to the setting of split p-adic groups and their pure inner twists. Our work generalizes a construction of Moeglin--Waldspurger for orthogonal groups. In my talk, I will introduce some of these ideas via examples.
