Geodesic
Weyl shift of $q$-oscillator and $q$-polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 307-315

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A unitary Weyl operator $U_q(w)$ that realizes a "$q$-shift" automorphism for the $q$-oscillator is found. Explicit expressions for the matrix elements and coherent states are found. It is shown that the Weyl $q$-operator generates isospectral families of orthogonal polynomials that generalize the Charlier and Hermite polynomials. 
@article{TMF_1993_94_2_a9,
     author = {A. S. Zhedanov},
     title = {Weyl shift of $q$-oscillator and $q$-polynomials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {307--315},
     publisher = {mathdoc},
     volume = {94},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a9/}
}
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A. S. Zhedanov. Weyl shift of $q$-oscillator and $q$-polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 307-315. http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a9/