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A Multiplicative Property of Quantum Flag Minors II
Author(s) -
Caldero Philippe,
Marsh Bethany R.
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005174
Subject(s) - flag (linear algebra) , multiplicative function , mathematics , quantum , pure mathematics , combinatorics , algebra over a field , physics , quantum mechanics , mathematical analysis
Let U + be the plus part of the quantized enveloping algebra of a simple Lie algebra of type A n 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.