Volume 24, pp. 74-78, 2006.

q-orthogonal polynomials related to the quantum group Uq(so(5))

Alexander Rozenblyum

Abstract

Orthogonal polynomials in two discrete variables related to finite-dimensional irreducible representations of the quantum algebra $U_q({\bf so}(5))$ are studied. The polynomials we consider here can be treated as two-dimensional $q$-analogs of Krawtchouk polynomials. Some properties of these polynomials are investigated: the difference equation of the Sturm-Liouville type, the weight function, the corresponding eigenvalues including the explicit description of their multiplicities.

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Key words

quantum group, discrete orthogonal polynomials, eigenvalues

AMS subject classifications

33D80, 33C45

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