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

• 作者: M. Francisca Yanez
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: Q-模拟 Gln 谐波分析 氡气 滤清 锡 运营商 GEL
• 年，卷（期）: 2015,（2）
• 页码范围: 189-210
• 页数: 22页
• 分类号: O157.1
• 语种: 中文

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.