Harmonic Analysis of Radon Filtrations for S(n) and GL(n,q)

2009/01/18 by M. Francisca Yáñez, M. Francisca Yanez, Yanez, M. Francisca
Mathematics · Medicine · #Occupational and environmental lung diseases #math.GR #math.RT #msc:20C15 #msc:20C30 #msc:20C33

paper · pdf · doi:10.48550/arxiv.0901.2669

28 pages

arxiv created 2009/01/18 · arxiv updated 2009/12/01

Abstract

We 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.

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