XXXVII Workshop on Geometric Methods in Physics | 1-7.07.2018 |

VII School on Geometry and Physics | 25-29.06.2018 |

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## Jiří Hrivnak## Generating functions of two-variable Chebyshev polynomialsFourteen classes of generalized Chebyshev polynomials related to rank two Lie algebras are introduced. The variables of the polynomials are given via the classical characters of the Lie algebras. There exist two, four and eight classes for the algebras $A_2$, $C_2$ and $G_2$, respectively. The admissible weight shift, which permits the constructions of the eight classes of $C_2$, directly generalizes the four classical kinds of Chebyshev polynomials. Generating functions of all fourteen classes are constructed in the form of rational polynomial functions of four variables. Explicit evaluating formulas, which calculate any given polynomial using addition and multiplication only, are derived and linked to the incomplete exponential Bell polynomials. This is a joint work with Tomasz Czyżycki and Jiří Patera. |

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University of Bialystok |

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