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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.


Classification of discrete series by minimal $K$-type
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by Rajagopalan Parthasarathy
Represent. Theory 19 (2015), 167-185
Published electronically: October 7, 2015


Following the proof by Hecht and Schmid of Blattner’s conjecture for $K$ multiplicities of representations belonging to the discrete series it turned out that some results which were earlier known with some hypothesis on the Harish-Chandra parameter of the discrete series representation could be extended removing those hypotheses. For example this was so for the geometric realization problem. Occasionally a few other results followed by first proving them for Harish-Chandra parameters which are sufficiently regular and then using Zuckerman translation functors, wall crossing methods, etc. Recently, Hongyu He raised the question (private communication) of whether the characterization of a discrete series representation by its lowest $K$-type, which was proved by this author and R. Hotta with some hypothesis on the Harish-Chandra parameter of the discrete series representations, can be extended to all discrete series representations excluding none, using a combination of these powerful techniques. In this article we will answer this question using Dirac operator methods and a result of Susana Salamanca-Riba.
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Bibliographic Information
  • Rajagopalan Parthasarathy
  • Affiliation: Raja Ramanna Fellow Bharathiar University Coimbatore
  • Email:
  • Received by editor(s): July 29, 2014
  • Received by editor(s) in revised form: December 4, 2014, and August 14, 2015
  • Published electronically: October 7, 2015
  • Additional Notes: This research was supported by Raja Ramanna Fellowship from DAE
    The author thanks the referee for suggestions to improve the article by addressing the case of general groups of Harish-Chandra class. His comments on the initial proof of Theorem 1.1 in Section 3 have greatly helped in adding considerable clarity to the original submission.
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 167-185
  • MSC (2010): Primary 22E46; Secondary 22D30
  • DOI:
  • MathSciNet review: 3405535