Big q-Laguerre and q-Meixner polynomials and representations of the quantum algebra Uq(su1,1)
Por:
Atakishiyev M.N., Atakishhev N.M., Klimyk A.U.
Publicada:
1 ene 2003
Resumen:
Diagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra Uq(su 1,1) is studied. Spectrum and eigenfunctions of this operator are explicitly found. These eigenfunctions, when normalized, constitute an orthonormal basis in the representation space. The initial Uq(su 1,1) basis and the basis of these eigenfunctions are interconnected 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 Mn(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 the q-Meixner polynomials Mn(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.
Filiaciones:
Atakishiyev M.N.:
Instituto de Matemáticas, UNAM, CP 62210 Cuernavaca, Morelos, Mexico
Atakishhev N.M.:
Instituto de Matemáticas, UNAM, CP 62210 Cuernavaca, Morelos, Mexico
Klimyk A.U.:
Instituto de Matemáticas, UNAM, CP 62210 Cuernavaca, Morelos, Mexico
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