Geodesic
Weyl shift of $q$-oscillator and $q$-polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 2, pp. 307-315 
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/
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     title = {Weyl shift of $q$-oscillator and $q$-polynomials},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_2_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Perelomov A. M., Obobschennye kogerentnye sostoyaniya i ikh primeneniya, Nauka, M., 1987 | MR

[2] Zhedanov A. S., J. Phys.(A), 24:19 (1991), L1129–L1133 | MR

[3] Aric M., Coon D., J. Math. Phys., 17:4 (1976), 524–527 | DOI | MR

[4] Jannussis A. et.al., Hadronic J., 6:6 (1983), 1653–1686 | MR

[5] Biedenharn L. C., J. Phys.(A), 22:18 (1989), L983–L986 | MR

[6] Damaskinskii E. V., Kulish P. P., Zapiski nauchn. semin. LOMI, 189, 1991, 37–74 ; J. Phys.(A), 23:9 (1990), L415–L419 | MR | MR | Zbl

[7] Gasper G., Rahman M., Basic hipergeometric series, Cambridge University Press, 1990 | MR | Zbl

[8] Nikiforov A. F., Suslov S. K., Uvarov V. B., Klassicheskie ortogonalnye polinomy diskretnoi peremennoi, Nauka, M., 1985 | MR

[9] Granovskii Ya. I., Zhedanov A. S., Izv. vuzov. Fizika., 5 (1986), 60–66 | MR

[10] Feinsilver P., Acta Appl. Mathem., 19:2 (1990), 207–251 | DOI | MR | Zbl

[11] Atakishiev N. M., Suslov S. K., TMF, 85:1 (1990), 64–73 ; 87:1 (1991), 154–156 | MR | Zbl | MR | Zbl

[12] Zhedanov A. S., TMF, 89:2 (1991), 190–204 | MR

[13] Zhedanov A. S., Phys. Lett.(A), 1992, to appear | MR