2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216466We present a unified approach to the study of Radon transforms related to symmetric groups and to general linear groups GL(n,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.28 pagesRepresentation TheoryGroup Theory20C33, 20C30, 20C15text