Quantized Chebyshev polynomials and cluster characters with coefficients
arXiv:0908.4014 · doi:10.1007/s10801-009-0198-8
Abstract
We introduce quantized Chebyshev polynomials as deformations of generalized Chebyshev polynomials previously introduced by the author in the context of acyclic coefficient-free cluster algebras. We prove that these quantized polynomials arise in cluster algebras with principal coefficients associated to acyclic quivers of infinite representation types and equioriented Dynkin quivers of type . We also study their interactions with bases and especially canonically positive bases in affine cluster algebras.
28 pages. Final version, to appear in Journal of Algebraic Combinatorics