We present a unified approach to the study of Radon transforms related to the group Sn and its q-analogue GLn（q）. In both cases, in a uniform way, we define a sequence of generMized Radon transforms that are intertw...We present a unified approach to the study of Radon transforms related to the group Sn and its q-analogue GLn（q）. In both cases, in a uniform way, we define a sequence of generMized Radon transforms that are intertwining operators for natural representa- tions associated to Gel＇land spaces for our groups. This sequence and the sequence of their adjoint enable us to decompose in a recursive way these natural representations into irreducibles and to compute explicitly the associated spherical functions. Our methods and results rely then strongly on q-analogy.展开更多
文摘We present a unified approach to the study of Radon transforms related to the group Sn and its q-analogue GLn（q）. In both cases, in a uniform way, we define a sequence of generMized Radon transforms that are intertwining operators for natural representa- tions associated to Gel＇land spaces for our groups. This sequence and the sequence of their adjoint enable us to decompose in a recursive way these natural representations into irreducibles and to compute explicitly the associated spherical functions. Our methods and results rely then strongly on q-analogy.
