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A MULTIPLICATIVE PROPERTY OF QUANTUM FLAG MINORS II

Published online by Cambridge University Press:  24 May 2004

PHILIPPE CALDERO  and
ROBERT MARSH
PHILIPPE CALDERO
Affiliation:
Département de Mathématiques, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, Francecaldero@igd.univ-lyon1.fr
ROBERT MARSH
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdomrjm25@mcs.le.ac.uk
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Abstract

Let $U^+$ be the plus part of the quantized enveloping algebra of a simple Lie algebra of type $A_n$ and let $\mathcal{B}^*$ be the dual canonical basis of $U^+$. Let $b$, $b'$ be in $\mathcal{B}^*$, and suppose that one of the two elements is a $q$-commuting product of quantum flag minors. It is shown that $b$ and $b'$ are multiplicative if and only if they $q$-commute.

Keywords

17B37
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 608 - 622
Copyright
The London Mathematical Society 2004

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Footnotes

This work was supported by an EC grant of the TMR network “Algebraic Lie representations”, contract ERB FMTX-CT97-0100, which supported the visit of both authors to Wuppertal in October 2001, the first author's visit to Leicester in August 2002, and the study leave of the second author at the University of Leicester in the autumn of 2002.