Geodesic
Quantized Chebyshev polynomials and cluster characters with coefficients
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 4, pp. 501-532.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\mathbb A$ mathbbA . We also study their interactions with bases and especially canonically positive bases in affine cluster algebras.
Keywords: keywords cluster algebras, quantized Chebyshev polynomials, principal coefficients, regular components, orthogonal polynomials 
@article{JAC_2010__31_4_a3,
     author = {Dupont, Gr\'egoire},
     title = {Quantized {Chebyshev} polynomials and cluster characters with coefficients},
     journal = {Journal of Algebraic Combinatorics},
     pages = {501--532},
     publisher = {mathdoc},
     volume = {31},
     number = {4},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_4_a3/}
}
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Dupont, Grégoire. Quantized Chebyshev polynomials and cluster characters with coefficients. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 4, pp. 501-532. http://geodesic.mathdoc.fr/item/JAC_2010__31_4_a3/