XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Tomasz Czyżycki## Generalized Multivariate Chebyshev PolynomialsClasses of generalized Chebyshev polynomials related to root systems of simple Lie algebras are introduced. The variables of the polynomials are given via the classical character functions of the Lie algebras. Depending on the type of the algebra there exist two, four or eight polynomial classes. The admissible shift of the weight lattice, which permits the constructions of the eight classes of the classical series $C_n$, directly generalizes the four classical kinds of Chebyshev polynomials. The discrete orthogonality relations over the sets of the generalized Chebyshev nodes are presented in detail and the forms of generating functions and cubature rules are discussed. This is a joint work with Jiri Hrivnak. |

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University of Bialystok |

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