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Abstract: Recursive algebraic construction of two infinite families of polynomials in$n$ variables is proposed as a uniform method applicable to every semisimpleLie group of rank $n$. Its result recognizes Chebyshev polynomials of the firstand second kind as the special case of the simple group of type $A 1$. Theobtained not Laurent-type polynomials are proved to be equivalent to thepartial cases of the Macdonald symmetric polynomials. Basic relation betweenthe polynomials and their properties follow from the corresponding propertiesof the orbit functions, namely the orthogonality and discretization. Recurrencerelations are shown for the Lie groups of types $A 1$, $A 2$, $A 3$, $C 2$,$C 3$, $G 2$, and $B 3$ together with lowest polynomials.

Autor: Maryna Nesterenko, Jiri Patera, Agnieszka Tereszkiewicz

Fuente: https://arxiv.org/

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