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Journal of the London Mathematical Society 2004 69(3):608-622; doi:10.1112/S0024610704005174
© 2004 by London Mathematical Society
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© The London Mathematical Society

A Multiplicative Property of Quantum Flag Minors II

Philippe Caldero and Robert Marsh

Département de Mathématiques, Université Claude Bernard Lyon I 69622 Villeurbanne Cedex, France, caldero{at}igd.univ-lyon1.fr
Department of Mathematics, University of Leicester University Road, Leicester LE1 7RH, United Kingdom, rjm25{at}mcs.le.ac.uk

Received 18 February 2003. Revision received 7 November 2003.

Let U+ be the plus part of the quantized enveloping algebra of a simple Lie algebra of type An and let B* be the dual canonical basis of U+. Let b, b' be in 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.


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