Abstract
In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomials h˜n,α(x;q), introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a q-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce q-Schrödinger operators and we give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra suq(1,1), using the generators associated with a q-deformed generalized para-Bose oscillator.
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