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The Ramanujan Journal

, Volume 46, Issue 1, pp 127–149 | Cite as

An algebraic interpretation of the q-Meixner polynomials

  • Julien Gaboriaud
  • Luc Vinet
Article
  • 67 Downloads

Abstract

An algebraic interpretation of the q-Meixner polynomials is obtained. It is based on representations of \({\mathscr {U}}_q({\mathfrak {su}}(1,1))\) on q-oscillator states with the polynomials appearing as matrix elements of unitary q-pseudorotation operators. These operators are built from q-exponentials of the \({\mathscr {U}}_q({\mathfrak {su}}(1,1))\) generators. The orthogonality, recurrence relation, difference equation, and other properties of the q-Meixner polynomials are systematically obtained in the proposed framework.

Keywords

q-Meixner polynomials \({\mathscr {U}}_q{\mathfrak {su}}(1, 1)\) quantum algebra q-Oscillators 

Mathematics Subject Classification

33D45 81R50 

Notes

Acknowledgements

The authors would like to thank V. X. Genest, T. Koornwinder, M. E. H. Ismail, and A. Zhedanov for useful remarks and helpful discussions. J. G. holds an Alexander-Graham-Bell Graduate Scholarship from the Natural Sciences and Engineering Research Council (NSERC) of Canada. The research of L. V. was supported in part by the NSERC.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Centre de Recherches MathématiquesUniversité de MontréalMontrealCanada

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