{"title":"On the Connes–Kasparov isomorphism, II","authors":"","doi":"10.1007/s11537-024-2221-1","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>This is the second of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to C*-algebraic Morita equivalence, and the verification of the Connes–Kasparov conjecture in operator K-theory for these groups. In Part I we presented the Morita equivalence and the Connes–Kasparov morphism. In this part we shall compute the morphism using David Vogan’s description of the tempered dual. In fact we shall go further by giving a complete representation-theoretic description and parametrization, in Vogan’s terms, of the essential components of the tempered dual, which carry the <em>K</em>-theory of the tempered dual.</p>","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11537-024-2221-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
This is the second of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to C*-algebraic Morita equivalence, and the verification of the Connes–Kasparov conjecture in operator K-theory for these groups. In Part I we presented the Morita equivalence and the Connes–Kasparov morphism. In this part we shall compute the morphism using David Vogan’s description of the tempered dual. In fact we shall go further by giving a complete representation-theoretic description and parametrization, in Vogan’s terms, of the essential components of the tempered dual, which carry the K-theory of the tempered dual.
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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