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Abstract: Let U q be the quantum group associated to a Lie algebra g of rank n. The negative part U \Gamma q of U q has a canonical basis B with favourable properties (see Kashiwara [3] and Lusztig [6, x14.4.6]). 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 the Weyl group of g. We describe the authors' recent work establishing close relationships between the Lusztig cones, canonical... (Update)
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BibTeX entry: (Update)
@misc{ carter-canonical,
author = "Roger Carter and Robert Marsh",
title = "Canonical Bases and Piecewise-linear Combinatorics",
url = "citeseer.ist.psu.edu/carter00canonical.html" }
Citations (may not include all citations):76 Introduction to Quantum Groups (context) - Lusztig - 1993
64 analogue of universal enveloping algebras (context) - Kashiwara, bases et al. - 1991
34 Canonical bases arising from quantized enveloping algebras (context) - Lusztig - 1990
23 Parametrizations of canonical bases and totally positive mat.. (context) - Berenstein, Fomin et al. - 1996
2 Introduction to quantized enveloping algebras (context) - Lusztig - 1992
1 Lusztig cones and canonical basis elements for the quantized.. (context) - Carter, Marsh et al.
1 More tight monomials in quantized enveloping algebras - Marsh - 1998
1 Rectangle diagrams for the Lusztig cones of quantized envelo.. (context) - Marsh
1 The Lusztig cone and the image of the Kashiwara map (context) - Premat - 1999
1 Canonical basis for type (context) - Xi - 1998
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