{"title":"无限维表示的大小","authors":"David A. Vogan","doi":"10.1007/s11537-017-1648-z","DOIUrl":null,"url":null,"abstract":"An infinite-dimensional representation π of a real reductive Lie group <i>G</i> can often be thought of as a function space on some manifold <i>X</i>. Although <i>X</i> is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of <i>X</i>. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent progress toward computing them.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"136 ","pages":"175-210"},"PeriodicalIF":1.8000,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The size of infinite-dimensional representations\",\"authors\":\"David A. Vogan\",\"doi\":\"10.1007/s11537-017-1648-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An infinite-dimensional representation π of a real reductive Lie group <i>G</i> can often be thought of as a function space on some manifold <i>X</i>. Although <i>X</i> is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of <i>X</i>. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent progress toward computing them.\",\"PeriodicalId\":54908,\"journal\":{\"name\":\"Japanese Journal of Mathematics\",\"volume\":\"136 \",\"pages\":\"175-210\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2017-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Japanese Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11537-017-1648-z\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11537-017-1648-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
An infinite-dimensional representation π of a real reductive Lie group G can often be thought of as a function space on some manifold X. Although X is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of X. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent progress toward computing them.
期刊介绍：
The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years.
An eminent international mathematics journal, the Japanese Journal of Mathematics has been published since 1924. It is an ideal resource for a wide range of mathematicians extending beyond a small circle of specialists.
The official journal of the Mathematical Society of Japan.
Devoted to authoritative research survey articles that will promote future progress in mathematics.
Gives new insight on topics of current interest from broad perspectives and/or reviews all major developments in an important area over many years.
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