On local gamma factors via Braverman-Kazhdan program

In this talk, we will discuss the local gamma factors that appear in the functional equations of local $L$ factors in the framework proposed by Braverman and Kazhdan. We will introduce some of the basic objects of this theory, focusing on the proposed generalization of the standard Fourier transform. The descent of this Fourier transform along parabolic subgroups allows us to establish multiplicativity for gamma factors. If time permits we also discuss the action of the generalized Fourier operator on representations in the test case where $G=\mathrm{GL}(2)$.