Title: Fourier transform on a cone and  minimal representations


Abstract: The classical Fourier  transform on L^2(V) for a vector space V commutes with the natural action of the orthogonal group O(V). This operator belongs to a family of operators, served by the minimal (Weil) representation of the  metaplectic group.

In the talk I will describe how the  minimal representation of an orthogonal group gives rise to a remarkable operator,  called Fourier transform on a cone. We shall see how analytic properties of this Fourier transform imply important properties of the minimal representation.  

This is joint work with D. Kazhdan.

Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=218ca6e1-d1b2-4505-8ebd-b116006ce1bc