The tree method for multidimensional <Emphasis Type="Italic">q</Emphasis>-Hahn and <Emphasis Type="Italic">q</Emphasis>-Racah polynomials |
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Authors: | Fabio Scarabotti |
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Institution: | 1.Dipartimento MeMoMat,Università degli Studi di Roma “La Sapienza”,Rome,Italy |
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Abstract: | We develop a tree method for multidimensional q-Hahn polynomials. We define them as eigenfunctions of a multidimensional q-difference operator and we use the factorization of this operator as a key tool. Then we define multidimensional q-Racah polynomials as the connection coefficients between different bases of q-Hahn polynomials. We show that our multidimensional q-Racah polynomials may be expressed as product of ordinary one-dimensional q-Racah polynomial by means of a suitable sequence of transplantations of edges of the trees. Our paper is inspired to the
classical tree methods in the theory of Clebsch–Gordan coefficients and of hyperspherical coordinates. It is based on previous
work of Dunkl, who considered two-dimensional q-Hahn polynomials. It is also related to a recent paper of Gasper and Rahman: we show that their multidimensional q-Racah polynomials correspond to a particular case of our construction. |
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