4 research outputs found
New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential
Using a realization of the q-exponential function as an infinite
multiplicative sereis of the ordinary exponential functions we obtain new
nonlinear connection formulae of the q-orthogonal polynomials such as
q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective
classical analogs.Comment: 14 page
Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]
Representations of the quantum superalgebra U_q[osp(1/2)] and their relations
to the basic hypergeometric functions are investigated. We first establish
Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the
representations having no classical counterparts are incorporated. Formulae for
these Clebsch-Gordan coefficients are derived, and it is observed that they may
be expressed in terms of the -Hahn polynomials. We next investigate
representations of the quantum supergroup OSp_q(1/2) which are not well-defined
in the classical limit. Employing the universal T-matrix, the representation
matrices are obtained explicitly, and found to be related to the little
Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in
all cases. Using the Clebsch-Gordan coefficients derived here, we construct new
noncommutative spaces that are covariant under the coaction of the even
dimensional representations of the quantum supergroup OSp_q(1/2).Comment: 16 pages, no figure