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

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

2009-01-18

arxiv.org/abs/0901.2669v1

Mathematics

Representation Theory

28 pages

Scientific paper

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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