Canonical Bases and Piecewise-linear Combinatorics

Abstract

Let Uq be the quantum group associated to a Lie algebra g of rank n. The negative part U q of Uq has a canonical basis B with favourable properties (see Kashiwara [3] and Lusztig [6, §14.4.6]). The approaches of Lusztig and Kashiwara lead to a set of alternative parametrizations of the canonical basis, one for each reduced expression for the longest word in… (More)

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