## Communications in Mathematical Analysis

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

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

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

#### 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