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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.


The Dynkin diagram $R$-group
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by Dana Pascovici
Represent. Theory 5 (2001), 1-16
Published electronically: January 18, 2001


We define an abelian group from the Dynkin diagram of a split real linear Lie group with abelian Cartan subgroups, $G$, and show that the $R_{\delta , 0}$-groups defined by Knapp and Stein are subgroups of it. The proof relies on Vogan’s approach to the $R$-groups. The $R$-group of a Dynkin diagram is easily computed just by looking at the diagram, and so it gives, for instance, quick proofs of the fact that the principal series with zero infinitesimal character of the split groups $E_6$, $E_8$, $G_2$ or $F_4$ are irreducible. The Dynkin diagram subgroup also implicitly describes a small Levi subgroup, which we hope might play a role in computing regular functions on principal nilpotent orbits. We present in the end a conjecture and some evidence in this direction.
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Bibliographic Information
  • Dana Pascovici
  • Affiliation: Department of Mathematics, Purdue University, MATH 602, West Lafayette, Indiana 47906
  • Email:
  • Received by editor(s): May 31, 2000
  • Received by editor(s) in revised form: October 10, 2000
  • Published electronically: January 18, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 1-16
  • MSC (2000): Primary 22E46; Secondary 22E45
  • DOI:
  • MathSciNet review: 1826426