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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

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1435-5345
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Volume 2015, Issue 703

Issues

Classification of symmetric pairs with discretely decomposable restrictions of (𝔤,K)-modules

Toshiyuki Kobayashi
  • Kavli IPMU (WPI) and Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, 153-8914 Tokyo, Japan
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/ Yoshiki Oshima
Published Online: 2013-07-13 | DOI: https://doi.org/10.1515/crelle-2013-0045

Abstract

We give a complete classification of reductive symmetric pairs (𝔤,𝔥) with the following property: there exists at least one infinite-dimensional irreducible (𝔤,K)-module X that is discretely decomposable as an (𝔥,HK)-module. We investigate further if such X can be taken to be a minimal representation, a Zuckerman derived functor module A𝔮(λ), or some other unitarizable (𝔤,K)-module. The tensor product π1π2 of two infinite-dimensional irreducible (𝔤,K)-modules arises as a very special case of our setting. In this case, we prove that π1π2 is discretely decomposable if and only if π1 and π2 are simultaneously highest weight modules.

About the article

Received: 2012-12-09

Published Online: 2013-07-13

Published in Print: 2015-06-01


Funding Source: JSPS

Award identifier / Grant number: Grant-in-Aid for Scientific (A) (25247006)

Funding Source: JSPS

Award identifier / Grant number: Grant-in-Aid for JSPS Fellows


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 703, Pages 201–223, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0045.

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[1]
T. Kobayashi and T. Matsuki
Transformation Groups, 2014, Volume 19, Number 2, Page 457

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