Harmonic oscillator group and Laguerre 2D polynomials

In this paper, we derive some generating relations involving Laguerre 2D polynomials (L2DP) Lm,n(U; z,z) of two variables with an arbitrary 2D matrix U as a parameter by relating these polynomials to the harmonic oscillator group G(0, 1). Certain special cases yielding inevitably many new and known generating relations for the polynomials related to L2DP are also discussed.