On cluster algebras arising from unpunctured surfaces II

Details On cluster algebras arising from unpunctured surfaces II On cluster algebras arising from unpunctured surfaces II

2008-09-15

arxiv.org/abs/0809.2593v2

Mathematics

Representation Theory

36 pages, 9 figures

Scientific paper

We study cluster algebras with principal and arbitrary coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of certain paths on a triangulation of the surface. As an immediate consequence, we prove the positivity conjecture of Fomin and Zelevinsky for these cluster algebras. Furthermore, we obtain direct formulas for F-polynomials and g-vectors and show that F-polynomials have constant term equal to 1. As an application, we compute the Euler-Poincar\'e characteristic of quiver Grassmannians in Dynkin type $A$ and affine Dynkin type $\tilde A$.

Affiliated with

Also associated with

No associations

Rating

On cluster algebras arising from unpunctured surfaces II 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 On cluster algebras arising from unpunctured surfaces II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On cluster algebras arising from unpunctured surfaces II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-636071