Compactly Supported Distributions on p-Adic Lie Groups

被引：0

作者：

Ban, Dubravka ^{[1
]}

Roberts, Jeremiah ^{[1
]}

机构：

[1] Southern Illinois Univ, Sch Math & Stat Sci, 1245 Lincoln Dr, Carbondale, IL 62901 USA

来源：

P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS | 2024年 / 16卷 / 03期

关键词：

p-adic Lie groups; Iwasawa algebra; distributions; Banach representation; principal series; Frobenius reciprocity; PRINCIPAL SERIES; REPRESENTATIONS;

D O I：

10.1134/S2070046624030014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a finite extension of Q(p) and let G be a p-adic Lie group. In this paper, we define the Iwasawa algebra K[[G]] and prove that it is isomorphic to the convolution algebra of compactly supported distributions on G. This has important applications in the theory of admissible representations of G on p-adic Banach spaces. In particular, we prove the Frobenius reciprocity for continuous principal series representations.

引用

页码：201 / 218

页数：18

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