Harmonic Analysis of Radon Filtrations for Sn and GLn(q)

Abstract

We present a unified approach to the study of Radon transforms related to symmetric groups and to general linear groups GLn(q), regarded as q−analogues of the former. In both cases, we define a sequence of generalized Radon transforms which are intertwining operators for natural representations associated to Gel’fand spaces for our groups. This sequence enables us to decompose in a recursive way these natural representations and to compute explicitly the associated spherical functions. Our methods and results are related by q−analogy.