Spherical Analysis Attached to Some m-Step Nilpotent Lie Group

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-02 DOI:10.1007/s00041-024-10076-0

Silvina Campos, José García, Linda Saal

引用次数: 0

Abstract

We introduce a family of generalized Gelfand pairs \((K_m,N_m)\) where \(N_m\) is an \(m+2\)-step nilpotent Lie group and \(K_m\) is isomorphic to the 3-dimensional Heisenberg group. We develop the associated spherical analysis computing the set of the spherical distributions and we obtain some results on the algebra of \(K_m\)-invariant and left invariant differential operators on \(N_m\).

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附属于某些 m 阶无势李群的球面分析

我们引入了广义格尔方对族 \((K_m,N_m)\)，其中 \(N_m\) 是一个 \(m+2\)- 步零potent Lie 群，而 \(K_m\) 与三维海森堡群同构。我们发展了计算球面分布集合的相关球面分析，并得到了一些关于 \(K_m\) 上不变和左不变微分算子代数的结果。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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