Quantum algebra from generalized q-Hermite polynomials

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-Schrodinger 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 su q ( 1 , 1 ) , using the generators associated with a q-deformed generalized para-Bose oscillator.