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

作　　者：M. Francisca Yanez 

机构地区：[1]Escuela de Pregrado, Facultad de Ciencias Qufmicas y Farmaceuticas Universidad de Chile, Sergio Livingston 1007, Santiago, Chile

出　　处：《Algebra Colloquium》2015年第2期189-210,共22页代数集刊（英文版）

摘　　要：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.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.

关 键 词：Radon transform spherical function Q-ANALOGUE Gel＇fand space natural representation 

分 类 号：O157.1[理学—数学] TS201.24[理学—基础数学]