Canonical Bases and Piecewise-linear Combinatorics

Details Canonical Bases and Piecewise-linear Combinatorics Canonical Bases and Piecewise-linear Combinatorics

2000-08-08

arxiv.org/abs/math/0008059v1

Mathematics

Quantum Algebra

12 pages, 13 figures, uses pictex

Scientific paper

Let U be the quantum group associated to a Lie algebra g of rank n. The negative part U^- of U has a canonical basis B with favourable properties, introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig 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 basis elements and the regions of linearity of reparametrization functions arising from the above parametrizations in type A_4 and give some speculations for type A_n. Keywords: Quantum group, Lie algebra, Canonical basis, Tight monomials, Weyl group, Piecewise-linear functions.

Affiliated with

Also associated with

No associations

Rating

Canonical Bases and Piecewise-linear Combinatorics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Canonical Bases and Piecewise-linear Combinatorics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical Bases and Piecewise-linear Combinatorics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-429293