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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.


Category $\mathcal O$: Quivers and endomorphism rings of projectives
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by Catharina Stroppel
Represent. Theory 7 (2003), 322-345
Published electronically: August 8, 2003


We describe an algorithm for computing quivers of category $\mathcal O$ of a finite dimensional semisimple Lie algebra. The main tool for this is Soergel’s description of the endomorphism ring of the antidominant indecomposable projective module of a regular block as an algebra of coinvariants. We give explicit calculations for root systems of rank 1 and 2 for regular and singular blocks and also quivers for regular blocks for type $A_3$. The main result in this paper is a necessary and sufficient condition for an endomorphism ring of an indecomposable projective object of $\mathcal O$ to be commutative. We give also an explicit formula for the socle of a projective object with a short proof using Soergel’s functor $\mathbb V$ and finish with a generalization of this functor to Harish-Chandra bimodules and parabolic versions of category $\mathcal O$.
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Bibliographic Information
  • Catharina Stroppel
  • Affiliation: Mathematische Fakultät, Universität Freiburg, Germany
  • Email: and
  • Received by editor(s): January 7, 2002
  • Received by editor(s) in revised form: April 7, 2003, and June 10, 2003
  • Published electronically: August 8, 2003
  • Additional Notes: The author was partially supported by EEC TMR-Network ERB FMRX-CT97-0100
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 322-345
  • MSC (2000): Primary 17B10, 16G20
  • DOI:
  • MathSciNet review: 2017061