Krawtchouk Polynomials, a Unification of Two Different Group Theoretic Interpretations

The canonical matrix elements of irreducible unitary representations of $SU(2)$ are written as Krawtchouk polynomials, with the orthogonality being the row orthogonality for the unitary representation matrix. Dunkl's interpretation of Krawtchouk polynomials as spherical functions on wreath prod...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 13; no. 6; pp. 1011 - 1023
Main Author Koornwinder, Tom H.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.11.1982
Subjects
Polynomials
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Summary:The canonical matrix elements of irreducible unitary representations of $SU(2)$ are written as Krawtchouk polynomials, with the orthogonality being the row orthogonality for the unitary representation matrix. Dunkl's interpretation of Krawtchouk polynomials as spherical functions on wreath products of symmetric groups is generalized to the case of intertwining functions. A conceptual unification is given of these two group theoretic interpretations of Krawtchouk polynomials.
ISSN:0036-1410
1095-7154
DOI:10.1137/0513072