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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.


Highest weight categories arising from Khovanov’s diagram algebra III: category $\mathcal {O}$
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by Jonathan Brundan and Catharina Stroppel
Represent. Theory 15 (2011), 170-243
Published electronically: March 7, 2011


We prove that integral blocks of parabolic category $\mathcal {O}$ associated to the subalgebra $\mathfrak {gl}_m(\mathbb {C}) \oplus \mathfrak {gl}_n(\mathbb {C})$ of $\mathfrak {gl}_{m+n}(\mathbb {C})$ are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although this result is in principle known, the existing proof is quite indirect, going via perverse sheaves on Grassmannians. Our new approach is completely algebraic, exploiting Schur-Weyl duality for higher levels. As a by-product we get a concrete combinatorial construction of $2$-Kac-Moody representations in the sense of Rouquier corresponding to level two weights in finite type $A$.
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Bibliographic Information
  • Jonathan Brundan
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • Email:
  • Catharina Stroppel
  • Affiliation: Department of Mathematics, University of Bonn, 53115 Bonn, Germany
  • Email:
  • Received by editor(s): July 15, 2009
  • Received by editor(s) in revised form: June 22, 2010, and June 26, 2010
  • Published electronically: March 7, 2011
  • Additional Notes: The first author was supported in part by NSF grant no. DMS-0654147
    The second author was supported by the NSF and the Minerva Research Foundation DMS-0635607.
  • © Copyright 2011 American Mathematical Society
  • Journal: Represent. Theory 15 (2011), 170-243
  • MSC (2010): Primary 17B10, 16S37
  • DOI:
  • MathSciNet review: 2781018