{"title":"关于k不变函数的李代数","authors":"I. Toure, Kinvi Kangni","doi":"10.1215/KJM/1250271320","DOIUrl":null,"url":null,"abstract":"Let G be a locally compact group and let K be a compact subgroup of Aut ( G ), the group of automorphisms of G . ( G, K ) is a Gelfand pair if the algebra L 1 K ( G ) of K-invariant integrable functions on G is commu-tative under convolution. In this paper, we give some charactezations of this algebra in the nilpotent case, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in [1] and obtain a new criterion for Gelfand pairs.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"847-855"},"PeriodicalIF":0.0000,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On lie algebras of K-invariant functions\",\"authors\":\"I. Toure, Kinvi Kangni\",\"doi\":\"10.1215/KJM/1250271320\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a locally compact group and let K be a compact subgroup of Aut ( G ), the group of automorphisms of G . ( G, K ) is a Gelfand pair if the algebra L 1 K ( G ) of K-invariant integrable functions on G is commu-tative under convolution. In this paper, we give some charactezations of this algebra in the nilpotent case, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in [1] and obtain a new criterion for Gelfand pairs.\",\"PeriodicalId\":50142,\"journal\":{\"name\":\"Journal of Mathematics of Kyoto University\",\"volume\":\"48 1\",\"pages\":\"847-855\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics of Kyoto University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1215/KJM/1250271320\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics of Kyoto University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1215/KJM/1250271320","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
设G是一个局部紧群设K是Aut (G)的紧子群，G的自同构群。如果G上K不变可积函数的代数l1k (G)在卷积下是可交换的，则(G, K)是一个Gelfand对。本文给出了该代数在幂零情况下的一些性质，推广了C. Benson, J. Jenkins, G. Ratcliff在[1]中得到的一些结果，得到了Gelfand对的一个新判据。
Let G be a locally compact group and let K be a compact subgroup of Aut ( G ), the group of automorphisms of G . ( G, K ) is a Gelfand pair if the algebra L 1 K ( G ) of K-invariant integrable functions on G is commu-tative under convolution. In this paper, we give some charactezations of this algebra in the nilpotent case, which generalize some results obtained by C. Benson, J. Jenkins, G. Ratcliff in [1] and obtain a new criterion for Gelfand pairs.
期刊介绍：
Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.
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