Communications in Mathematical Analysis

Meixner Polynomials and Representations of the 3D Lorentz Group SO(2,1)

N. M. Atakishiyev, A. M. Jafarova, and E. I. Jafarov

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Abstract

We argue that the Meixner polynomials of a discrete variable are actually “encoded” within appropriate infinite-dimensional irreducible unitary representations of the three-dimensional Lorentz group SO(2,1). Hence discrete series of irreducible unitary representation spaces of the non compact group SO(2,1) can be naturally interpreted as discrete versions of the linear harmonic oscillator in standard non-relativistic quantum mechanics.

Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 14-23.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919752

Mathematical Reviews number (MathSciNet)
MR3292956

Zentralblatt MATH identifier
1323.33010

Subjects
Primary: 33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 39A70: Difference operators [See also 47B39] 47B39: Difference operators [See also 39A70]

Keywords
Meixner polynomials irreducible unitary representations Lorentz group harmonic oscillator

Citation

Atakishiyev, N. M.; Jafarova, A. M.; Jafarov, E. I. Meixner Polynomials and Representations of the 3D Lorentz Group SO(2,1). Commun. Math. Anal. 17 (2014), no. 2, 14--23. https://projecteuclid.org/euclid.cma/1418919752


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