Big q-Laguerre and q-Meixner polynomials and representations of the algebra U_q(su(1,1))

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dc.creatorAtakishiyev, M. N.
dc.creatorAtakishiyev, N. M.
dc.creatorKlimyk, A. U.
dc.date2003-06-12
dc.date.accessioned2026-07-07T10:50:40Z
dc.date.available2026-07-07T10:50:40Z
dc.descriptionDiagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra U_q(su(1,1)) is studied. Spectrum and eigenfunctions of this operator are found in an explicit form. These eigenfunctions, when normalized, constitute an orthonormal basis in the representation space. The initial U_q(su(1,1))-basis and the basis of eigenfunctions are interrelated by a matrix with entries, expressed in terms of big q-Laguerre polynomials. The unitarity of this connection matrix leads to an orthogonal system of functions, which are dual with respect to big q-Laguerre polynomials. This system of functions consists of two separate sets of functions, which can be expressed in terms of q-Meixner polynomials M_n(x;b,c;q) either with positive or negative values of the parameter b. The orthogonality property of these two sets of functions follows directly from the unitarity of the connection matrix. As a consequence, one obtains an orthogonality relation for q-Meixner polynomials M_n(x;b,c;q) with b<0. A biorthogonal system of functions (with respect to the scalar product in the representation space) is also derived.
dc.description15 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0306201
dc.identifierhttp://arxiv.org/abs/math/0306201
dc.identifierJ.Phys.A36:10335-10348,2003
dc.identifierdoi:10.1088/0305-4470/36/41/006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184609
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.titleBig q-Laguerre and q-Meixner polynomials and representations of the algebra U_q(su(1,1))
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