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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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A multiplicative property of quantum flag minors
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by Ph. Caldero PDF
Represent. Theory 7 (2003), 164-176 Request permission

Abstract:

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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Additional Information
  • Ph. Caldero
  • Affiliation: Institut Girard Desargues, Université Claude Bernard – Lyon 1, 69622 Villeurbanne Cedex, France
  • Email: caldero@desargues.univ-lyon1.fr
  • 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: https://doi.org/10.1090/S1088-4165-03-00156-0
  • MathSciNet review: 1973370