Cluster multiplication in regular components via generalized Chebyshev polynomials
arXiv:0801.3964
Abstract
We introduce a multivariate generalization of normalized Chebyshev polynomials of the second kind. We prove that these polynomials arise in the context of cluster characters associated to Dynkin quivers of type and representation-infinite quivers. This allows to obtain a simple combinatorial description of cluster algebras of type . We also provide explicit multiplication formulas for cluster characters associated to regular modules over the path algebra of any representation-infinite quiver.
20 pages. The article was entirely reorganized. Results were slightly generalized. Proofs are shortened. Some new results are proved