arXiv 0908.40142009-08-27math.RTmath.RA

Quantized Chebyshev polynomials and cluster characters with coefficients

G. Dupont

备注：: 28 pages. Final version, to appear in Journal of Algebraic Combinatorics
发表信息：: J. Algebr. Comb. (2010) 31:501--532
DOI：: 10.1007/s10801-009-0198-8

英文摘要：

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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