Orthogonal polynomials of compact simple Lie groups

Details Orthogonal polynomials of compact simple Lie groups Orthogonal polynomials of compact simple Lie groups

2010-01-20

arxiv.org/abs/1001.3683v4

Physics

Mathematical Physics

34 pages, some minor changes were done, to appear in IJMMS

Scientific paper

Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type $A_1$. The obtained not Laurent-type polynomials are proved to be equivalent to the partial cases of the Macdonald symmetric polynomials. Basic relation between the polynomials and their properties follow from the corresponding properties of the orbit functions, namely the orthogonality and discretization. Recurrence relations 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.

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