Spin Norm and Lambda Norm

2023/01/03 by Chengyu Du, Chao-Ping Dong, Du, Chengyu +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Bounded function #Combinatorics #FOS: Mathematics #Geometry #Infinitesimal #Lambda #Law #Mathematical analysis #Mathematical physics #Mathematics #Norm (philosophy) #Physics #Pi #Pure mathematics #Quantum mechanics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2301.01004

openalex publication_date 2023/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a K-type π, it is known that its spin norm (due to first-named author) is lower bounded by its lambda norm (due to Vogan). That is, ‖π‖_{\rm spin}≥ ‖π‖_{\rm lambda}. This note aims to describe for which π one can actually have equality. We apply the result to tempered Dirac series. In the case of real groups, we obtain that the tempered Dirac series are divided into #W¹ parts among all tempered modules with real infinitesimal characters.

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