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A family of multivariate orthogonal polynomials generalizing the standard(univariate) Charlier polynomials is shown to arise in the matrix elements ofthe unitary representation of the Euclidean group E(d) on oscillator states.These polynomials in d discrete variables are orthogonal on the product of dPoisson distributions. The accent is put on the d=2 case and the grouptheoretical setting is used to obtain the main properties of the polynomials:orthogonality and recurrence relations, difference equation, raising/loweringrelations, generating function, hypergeometric and integral representations andexplicit expression in terms of standard Charlier and Krawtchouk polynomials.The approach is seen to extend straightforwardly to an arbitrary number ofvariables. The contraction of SO(3) to E(2) is used to show that the bivariateCharlier polynomials correspond to a limit of the bivariate Krawtchoukpolynomials.

The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states