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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.


A multiplicative property of quantum flag minors
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by Ph. Caldero
Represent. Theory 7 (2003), 164-176
Published electronically: April 17, 2003


We study the multiplicative properties of the quantum dual canonical basis ${\mathcal B}^*$ associated to a semisimple complex Lie group $G$. We provide a subset $D$ of ${\mathcal B}^*$ such that the following property holds: if two elements $b$, $b’$ in ${\mathcal B}^*$ $q$-commute and if one of these elements is in $D$, then the product $bb’$ is in ${\mathcal B}^*$ up to a power of $q$, where $q$ is the quantum parameter. If $G$ is SL$_n$, then $D$ is the set of so-called quantum flag minors and we obtain a generalization of a result of Leclerc, Nazarov and Thibon.
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Bibliographic Information
  • Ph. Caldero
  • Affiliation: Institut Girard Desargues, Université Claude Bernard – Lyon 1, 69622 Villeurbanne Cedex, France
  • Email:
  • Received by editor(s): January 23, 2002
  • Received by editor(s) in revised form: November 8, 2002, and January 8, 2003
  • Published electronically: April 17, 2003
  • Additional Notes: Supported in part by the EC TMR network “Algebraic Lie Representations", contract no. ERB FMTX-CT97-0100
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 164-176
  • MSC (2000): Primary 17B10
  • DOI:
  • MathSciNet review: 1973370