{"title":"论黎曼对称空间的哈里什-钱德拉 Plancherel 定理","authors":"Bernhard Krötz, Job J. Kuit, Henrik Schlichtkrull","doi":"arxiv-2409.08113","DOIUrl":null,"url":null,"abstract":"In this article we give an overview of the Plancherel theory for Riemannian\nsymmetric spaces Z = G/K. In particular we illustrate recently developed\nmethods in Plancherel theory for real spherical spaces by explicating them for\nRiemannian symmetric spaces, and we explain how Harish-Chandra's Plancherel\ntheorem for Z can be proven from these methods.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Harish-Chandra's Plancherel theorem for Riemannian symmetric spaces\",\"authors\":\"Bernhard Krötz, Job J. Kuit, Henrik Schlichtkrull\",\"doi\":\"arxiv-2409.08113\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we give an overview of the Plancherel theory for Riemannian\\nsymmetric spaces Z = G/K. In particular we illustrate recently developed\\nmethods in Plancherel theory for real spherical spaces by explicating them for\\nRiemannian symmetric spaces, and we explain how Harish-Chandra's Plancherel\\ntheorem for Z can be proven from these methods.\",\"PeriodicalId\":501038,\"journal\":{\"name\":\"arXiv - MATH - Representation Theory\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08113\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08113","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文概述了黎曼对称空间 Z = G/K 的 Plancherel 理论。特别是,我们通过对黎曼对称空间的解释,说明了最近开发的用于实球面空间的 Plancherel 理论方法,并解释了如何通过这些方法证明 Z 的哈里什-钱德拉 Plancherel 定理。
On Harish-Chandra's Plancherel theorem for Riemannian symmetric spaces
In this article we give an overview of the Plancherel theory for Riemannian
symmetric spaces Z = G/K. In particular we illustrate recently developed
methods in Plancherel theory for real spherical spaces by explicating them for
Riemannian symmetric spaces, and we explain how Harish-Chandra's Plancherel
theorem for Z can be proven from these methods.