Fourier transform for prehomogeneous vector spaces over finite field (Developments in Representation Theory and Related Topics)

Abstract

Let (G, V) be a prehomogeneous vector space over a finite field of odd characteristic. Taniguchi and Thorne [2] developed a method to calculate explicit formulas of the Fourier transforms of any G-invariant functions over V. By means of their method, we calculate the Fourier transform of any G-invariant function for several prehomogeneous vector spaces.