Jan Schröer (Leeds)
Module theoretic interpretation of quantum minors
Let L be a the preprojective algebra of type An, and let B* be the dual canonical basis of the associated quantized algebra Uv-. The elements in B* are indexed by multisegments m. To each quantum minor bm* in B* we associate a L-module Lm (this is a laminated module in the sense of Ringel [3]). Our main result is the following:
Theorem. Let b*m and b*n be quantum flag minors. Then the following are equivalent:The proof of this theorem uses a combinatorial criterion due to Leclerc, Nazarov and Thibon [2] for two quantum flag minors to be multiplicative. For all missing definitions we refer to [1], [2] and [3].
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