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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the space of $K$-finite solutions to intertwining differential operators
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by Toshihisa Kubo and Bent Ørsted
Represent. Theory 23 (2019), 213-248
Published electronically: September 10, 2019


In this paper we give Peter–Weyl-type decomposition theorems for the space of $K$-finite solutions to intertwining differential operators between parabolically induced representations. Our results generalize a result of Kable for conformally invariant systems. The main idea is based on the duality theorem between intertwining differential operators and homomorphisms between generalized Verma modules. As an application we uniformly realize on the solution spaces of intertwining differential operators all small representations of $\widetilde {\mathrm {SL}}(3,\mathbb {R})$ attached to the minimal nilpotent orbit.
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Bibliographic Information
  • Toshihisa Kubo
  • Affiliation: Faculty of Economics, Ryukoku University, 67 Tsukamoto-cho, Fukakusa, Fushimi-ku, Kyoto 612-8577, Japan
  • MR Author ID: 965976
  • Email:
  • Bent Ørsted
  • Affiliation: Department of Mathematics, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
  • Email:
  • Received by editor(s): August 29, 2018
  • Received by editor(s) in revised form: June 5, 2019
  • Published electronically: September 10, 2019
  • Additional Notes: The first author was partially supported by JSPS Grant-in-Aid for Young Scientists (B) (JP26800052)
    Part of this research was conducted during a visit of the first author to the Department of Mathematics of Aarhus University and a visit of the second author to the Graduate School of Mathematical Sciences of the University of Tokyo.
  • © Copyright 2019 American Mathematical Society
  • Journal: Represent. Theory 23 (2019), 213-248
  • MSC (2010): Primary 22E46, 17B10
  • DOI:
  • MathSciNet review: 4001530