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An algebraic interpretation of the bivariate Krawtchouk polynomials isprovided in the framework of the 3-dimensional isotropic harmonic oscillatormodel. These polynomials in two discrete variables are shown to arise as matrixelements of unitary reducible representations of the rotation group in 3dimensions. Many of their properties are derived by exploiting thegroup-theoretic setting. The bivariate Tratnik polynomials of Krawtchouk typeare seen to be special cases of the general polynomials that correspond toparticular rotations involving only two parameters. It is explained how theapproach generalizes naturally to (d+1) dimensions and allows to interpretmultivariate Krawtchouk polynomials as matrix elements of SO(d+1) unitaryrepresentations. Indications are given on the connection with other algebraicmodels for these polynomials.

The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states