  The multivariate Meixner polynomials are shown to arise as matrix elements of
unitary representations of the $SO(d,1)$ group on oscillator states. These
polynomials depend on $d$ discrete variables and are orthogonal with respect to
the negative multinomial distribution. The emphasis is put on the bivariate
case for which the SO(2,1) connection is used to derive the main properties of
the polynomials: orthogonality relation, raising/lowering relations, generating
function, recurrence relations and difference equations as well as explicit
expressions in terms of standard (univariate) Krawtchouk and Meixner
polynomials. It is explained how these results generalize directly to $d$
variables.
