Compactly Supported Distributions on $$p$$ -Adic Lie Groups

IF 0.5 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS P-Adic Numbers Ultrametric Analysis and Applications Pub Date : 2024-07-30 DOI:10.1134/s2070046624030014

Dubravka Ban, Jeremiah Roberts

引用次数: 0

Abstract

Let $K$ be a finite extension of $\mathbb{Q}_p$ 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.

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关于$$p$$-自洽李群的紧凑支持分布

摘要让 $K$ 是 $\mathbb{Q}_p$ 的有限扩展，让 $G$ 是一个 $p$-adic Lie 群。在本文中，我们定义了岩泽代数 $K[[G]]$，并证明它与$G$上紧凑支持的分布的卷积代数同构。这在$p$-adic Banach 空间上的$G$的可容许表示理论中有重要应用。特别是，我们证明了连续主序列表示的弗罗贝尼斯互易性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

P-Adic Numbers Ultrametric Analysis and Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.