Cluster multiplication in regular components via generalized Chebyshev polynomials

Details Cluster multiplication in regular components via generalized Chebyshev polynomials Cluster multiplication in regular components via generalized Chebyshev polynomials

2008-01-25

arxiv.org/abs/0801.3964v2

Mathematics

Representation Theory

20 pages. The article was entirely reorganized. Results were slightly generalized. Proofs are shortened. Some new results are

Scientific paper

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 $\mathbb A$ and representation-infinite quivers. This allows to obtain a simple combinatorial description of cluster algebras of type $\mathbb A$. We also provide explicit multiplication formulas for cluster characters associated to regular modules over the path algebra of any representation-infinite quiver.

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