Quantized Chebyshev polynomials and cluster characters with coefficients

Details Quantized Chebyshev polynomials and cluster characters with coefficients Quantized Chebyshev polynomials and cluster characters with coefficients

2009-08-27

arxiv.org/abs/0908.4014v1

J. Algebr. Comb. (2010) 31:501--532

Mathematics

Representation Theory

28 pages. Final version, to appear in Journal of Algebraic Combinatorics

Scientific paper

10.1007/s10801-009-0198-8

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 $\mathbb A$. We also study their interactions with bases and especially canonically positive bases in affine cluster algebras.

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