More on the q-oscillator algebra and q-orthogonal polynomials
Roberto Floreanini, Jean LeTourneux, Luc Vinet
Abstract
Properties of certain q-orthogonal polynomials are connected to the q-oscillator algebra. The Wall and q-Laguerre polynomials are shown to arise as matrix elements of q-exponentials of the generators in a representation of this algebra. A realization is presented where the continuous q-Hermite polynomials form a basis of the representation space. Various identities are interpreted within this model. In particular, the connection formula between the continuous big q-Hermite polynomials and the continuous q-Hermite polynomials is thus obtained, and two generating functions for these last polynomials are algebraically derived.
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