{"title":"多数化和球面函数","authors":"Colin S. McSwiggen, Jonathan Novak","doi":"10.1093/IMRN/RNAA390","DOIUrl":null,"url":null,"abstract":"Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In this paper, we consider a generalized notion of majorization associated to an arbitrary root system $\\Phi,$ and show that it admits a natural characterization in terms of the values of spherical functions on any Riemannian symmetric space with restricted root system $\\Phi.$","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Majorization and Spherical Functions\",\"authors\":\"Colin S. McSwiggen, Jonathan Novak\",\"doi\":\"10.1093/IMRN/RNAA390\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In this paper, we consider a generalized notion of majorization associated to an arbitrary root system $\\\\Phi,$ and show that it admits a natural characterization in terms of the values of spherical functions on any Riemannian symmetric space with restricted root system $\\\\Phi.$\",\"PeriodicalId\":275006,\"journal\":{\"name\":\"arXiv: Representation Theory\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/IMRN/RNAA390\",\"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: Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/IMRN/RNAA390","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In this paper, we consider a generalized notion of majorization associated to an arbitrary root system $\Phi,$ and show that it admits a natural characterization in terms of the values of spherical functions on any Riemannian symmetric space with restricted root system $\Phi.$
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