## A multiplicative property of quantum flag minors

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- by Ph. Caldero
- Represent. Theory
**7**(2003), 164-176 - DOI: https://doi.org/10.1090/S1088-4165-03-00156-0
- Published electronically: April 17, 2003
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## 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.## References

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## Bibliographic 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