无限维仿射群的表示

IF 0.2 Q4 MATHEMATICS

Methods of Functional Analysis and Topology Pub Date : 2020-06-21 DOI:10.31392/MFAT-NPU26_4.2020.06

Y. Kondratiev

{"title":"无限维仿射群的表示","authors":"Y. Kondratiev","doi":"10.31392/MFAT-NPU26_4.2020.06","DOIUrl":null,"url":null,"abstract":"We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":" ","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2020-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Representations of the Infinite-Dimensional Affine Group\",\"authors\":\"Y. Kondratiev\",\"doi\":\"10.31392/MFAT-NPU26_4.2020.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.\",\"PeriodicalId\":44325,\"journal\":{\"name\":\"Methods of Functional Analysis and Topology\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2020-06-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Methods of Functional Analysis and Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31392/MFAT-NPU26_4.2020.06\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods of Functional Analysis and Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31392/MFAT-NPU26_4.2020.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

引入了一个无限维仿射群，构造了它的不可约酉表示。我们的方法遵循Vershik, Gelfand和Graev对微分同构群所使用的方法，但由于该群不作用于相空间而进行了必要的修改。但是，可以在某些函数类上定义它的动作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Representations of the Infinite-Dimensional Affine Group

We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Methods of Functional Analysis and Topology MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.